Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133197 | C2 | semidirect |
| 2. C2×#20259310 | C2 | semidirect |
| 3. #27133047 | C2 | semidirect |
| 4. #27133018 | C2 | semidirect |
| 5. #27132886 | C2 | semidirect |
| 6. #27132879 | C2 | semidirect |
| 7. #27132821 | C2 | semidirect |
| 8. #27132816 | C2 | semidirect |
| 9. #27132804 | C2 | semidirect |
| 11. #431×C191 | C2 | semidirect |
| 14. C2×Dic764 | C22 | semidirect |
| 16. C2×#15690276 | C22 | semidirect |
| 19. #20259314 | C22 | semidirect |
| 24. #20259310 | C22 | semidirect |
| 28. C4×Dic382 | C22 | semidirect |
| 29. C4×D764 | C22 | semidirect |
| 34. #20259247 | C22 | semidirect |
| 35. #20259247 | C22 | semidirect |
| 39. C4⋊C8×C191 | C22 | semidirect |
| 42. C4×C8×C191 | C22 | semidirect |
| 143. C191 | #3211 | semidirect |
| 155. #431 | D191 | semidirect |
| 179. C4⋊C8 | C2×D191 | semidirect |
| 186. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| C2×#20259310 | 2 |
| #27133047 | 2 |
| #27133018 | 2 |
| #27132886 | 2 |
| #27132879 | 2 |
| #27132821 | 2 |
| #27132816 | 2 |
| #27132804 | 2 |
| #27132799 | 2 |
| #431×C191 | 2 |
| #3211 | 191 |