Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27133463 | C2 | semidirect |
| 2. C2×#20259348 | C2 | semidirect |
| 3. C2×#20259348 | C2 | semidirect |
| 4. #27133429 | C2 | semidirect |
| 5. #27132932 | C2 | semidirect |
| 6. #27132925 | C2 | semidirect |
| 7. #27132711 | C2 | semidirect |
| 8. #27132645 | C2 | semidirect |
| 9. C2×#100×C191 | C2 | semidirect |
| 13. #20259355 | C22 | semidirect |
| 15. #20259350 | C22 | semidirect |
| 22. C2×#15690275 | C22 | semidirect |
| 24. C2×#15690272 | C22 | semidirect |
| 25. #20259330 | C22 | semidirect |
| 30. #20259257 | C22 | semidirect |
| 31. #20259240 | C22 | semidirect |
| 32. #20259238 | C22 | semidirect |
| 36. #100×C191 | C22 | semidirect |
| 147. C191 | #3068 | semidirect |
| 157. C2×#100 | D191 | semidirect |
| 184. #100 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| C2×#20259348 | 2 |
| #27133429 | 2 |
| #27132932 | 2 |
| #27132925 | 2 |
| #27132711 | 2 |
| #27132645 | 2 |
| C2×#100×C191 | 2 |
| #3068 | 191 |