Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Frattini | C22 | C23×D389 |
| Fitting | C4×D4×C389 | C2 |
| hypercenter | C4×D4 | D389 |
| hypocenter | C389 | #525 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20261966 | C2 | semidirect |
| 2. C22×C4×D389 | C2 | semidirect |
| 3. #27159369 | C2 | semidirect |
| 4. #27159366 | C2 | semidirect |
| 5. #27159362 | C2 | semidirect |
| 6. #27159361 | C2 | semidirect |
| 7. #27159357 | C2 | semidirect |
| 8. #27159356 | C2 | semidirect |
| 9. #27159354 | C2 | semidirect |
| 10. #27159352 | C2 | semidirect |
| 11. C4×D1556 | C2 | semidirect |
| 12. C4×C22⋊D389 | C2 | semidirect |
| 13. C4×C22⋊D389 | C2 | semidirect |
| 14. #27159341 | C2 | semidirect |
| 15. C4×D4×C389 | C2 | semidirect |
| 18. C2×Dic778 | C22 | semidirect |
| 24. C2×C22⋊D389 | C22 | semidirect |
| 31. C2×C4×D389 | C22 | semidirect |
| 32. C4⋊Dic389 | C22 | semidirect |
| 33. #20261945 | C22 | semidirect |
| 34. #20261945 | C22 | semidirect |
| 35. #20261945 | C22 | semidirect |
| 36. #20261945 | C22 | semidirect |
| 38. C22⋊Dic389 | C22 | semidirect |
| 43. #20261943 | C22 | semidirect |
| 44. #20261943 | C22 | semidirect |
| 45. C4×Dic389 | C22 | semidirect |
| 48. C22×C4×C389 | C22 | semidirect |
| 49. C4⋊C4×C389 | C22 | semidirect |
| 51. C22⋊C4×C389 | C22 | semidirect |
| 52. C42×C389 | C22 | semidirect |
| 76. C4×D389 | D4 | semidirect |
| 92. C22×C389 | #41 | semidirect |
| 103. C2×D389 | #41 | semidirect |
| 122. C389 | #525 | semidirect |
| 137. C4×D4 | D389 | semidirect |
| 157. C22×C4 | C2×D389 | semidirect |
| 163. C4⋊C4 | C2×D389 | semidirect |
| 173. C22⋊C4 | C2×D389 | semidirect |
| 175. C42 | C2×D389 | semidirect |
| 225. C22 | #20261966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261966 | 2 |
| C22×C4×D389 | 2 |
| #27159369 | 2 |
| #27159366 | 2 |
| #27159362 | 2 |
| #27159361 | 2 |
| #27159357 | 2 |
| #27159356 | 2 |
| #27159354 | 2 |
| #27159352 | 2 |
| C4×D1556 | 2 |
| C4×C22⋊D389 | 2 |
| #27159341 | 2 |
| C4×D4×C389 | 2 |
| #525 | 389 |