Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27159364 | C2 | semidirect |
| 2. #27159363 | C2 | semidirect |
| 3. #27159362 | C2 | semidirect |
| 4. #27159362 | C2 | semidirect |
| 5. #27159361 | C2 | semidirect |
| 6. #27159360 | C2 | semidirect |
| 9. C22⋊Q8×C389 | C2 | semidirect |
| 11. C2×Dic778 | C22 | semidirect |
| 12. C2×Dic778 | C22 | semidirect |
| 16. C4⋊Dic389 | C22 | semidirect |
| 17. C4⋊Dic389 | C22 | semidirect |
| 18. #20261945 | C22 | semidirect |
| 19. #20261945 | C22 | semidirect |
| 20. #20261945 | C22 | semidirect |
| 26. C2×Q8×C389 | C22 | semidirect |
| 28. C4⋊C4×C389 | C22 | semidirect |
| 29. C4⋊C4×C389 | C22 | semidirect |
| 33. C22×D389 | Q8 | semidirect |
| 70. C389 | #543 | semidirect |
| 78. C22⋊Q8 | D389 | semidirect |
| 84. C2×Q8 | C2×D389 | semidirect |
| 94. C4⋊C4 | C2×D389 | semidirect |
| 95. C4⋊C4 | C2×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159364 | 2 |
| #27159363 | 2 |
| #27159362 | 2 |
| #27159361 | 2 |
| #27159360 | 2 |
| C2×#20261943 | 2 |
| C22⋊C4×D389 | 2 |
| C22⋊Q8×C389 | 2 |
| #543 | 389 |