Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
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×D353 |
| commutator, socle, cosocle | C22×C353 | C24 |
| Frattini | C22 | C23×D353 |
| Fitting | C4×D4×C353 | C2 |
| hypercenter | C4×D4 | D353 |
| hypocenter | C353 | #525 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19150737 | C2 | semidirect |
| 2. C22×C4×D353 | C2 | semidirect |
| 3. #26014977 | C2 | semidirect |
| 4. #26014974 | C2 | semidirect |
| 5. #26014970 | C2 | semidirect |
| 6. #26014969 | C2 | semidirect |
| 7. #26014965 | C2 | semidirect |
| 8. #26014964 | C2 | semidirect |
| 9. #26014962 | C2 | semidirect |
| 10. #26014960 | C2 | semidirect |
| 11. C4×D1412 | C2 | semidirect |
| 12. C4×C22⋊D353 | C2 | semidirect |
| 13. C4×C22⋊D353 | C2 | semidirect |
| 14. #26014949 | C2 | semidirect |
| 15. C4×D4×C353 | C2 | semidirect |
| 18. C2×Dic706 | C22 | semidirect |
| 24. C2×C22⋊D353 | C22 | semidirect |
| 31. C2×C4×D353 | C22 | semidirect |
| 32. C4⋊Dic353 | C22 | semidirect |
| 33. #19150716 | C22 | semidirect |
| 34. #19150716 | C22 | semidirect |
| 35. #19150716 | C22 | semidirect |
| 36. #19150716 | C22 | semidirect |
| 38. C22⋊Dic353 | C22 | semidirect |
| 43. #19150714 | C22 | semidirect |
| 44. #19150714 | C22 | semidirect |
| 45. C4×Dic353 | C22 | semidirect |
| 48. C22×C4×C353 | C22 | semidirect |
| 49. C4⋊C4×C353 | C22 | semidirect |
| 51. C22⋊C4×C353 | C22 | semidirect |
| 52. C42×C353 | C22 | semidirect |
| 76. C4×D353 | D4 | semidirect |
| 92. C22×C353 | #41 | semidirect |
| 103. C2×D353 | #41 | semidirect |
| 122. C353 | #525 | semidirect |
| 137. C4×D4 | D353 | semidirect |
| 157. C22×C4 | C2×D353 | semidirect |
| 163. C4⋊C4 | C2×D353 | semidirect |
| 173. C22⋊C4 | C2×D353 | semidirect |
| 175. C42 | C2×D353 | semidirect |
| 225. C22 | #19150737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150737 | 2 |
| C22×C4×D353 | 2 |
| #26014977 | 2 |
| #26014974 | 2 |
| #26014970 | 2 |
| #26014969 | 2 |
| #26014965 | 2 |
| #26014964 | 2 |
| #26014962 | 2 |
| #26014960 | 2 |
| C4×D1412 | 2 |
| C4×C22⋊D353 | 2 |
| #26014949 | 2 |
| C4×D4×C353 | 2 |
| #525 | 353 |