Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133234 | C2 | semidirect |
| 3. #27133005 | C2 | semidirect |
| 4. #27132988 | C2 | semidirect |
| 5. #27132909 | C2 | semidirect |
| 6. #27132892 | C2 | semidirect |
| 7. #27132816 | C2 | semidirect |
| 8. #27132804 | C2 | semidirect |
| 9. #408×C191 | C2 | semidirect |
| 10. C22×Dic382 | C22 | semidirect |
| 21. #20259301 | C22 | semidirect |
| 27. #20259281 | C22 | semidirect |
| 28. #20259256 | C22 | semidirect |
| 29. #20259254 | C22 | semidirect |
| 30. #20259247 | C22 | semidirect |
| 31. #20259247 | C22 | semidirect |
| 35. C2×M16×C191 | C22 | semidirect |
| 36. C22×C8×C191 | C22 | semidirect |
| 38. C22⋊C8×C191 | C22 | semidirect |
| 137. C191 | #3200 | semidirect |
| 147. #408 | D191 | semidirect |
| 153. C2×M16 | C2×D191 | semidirect |
| 154. C22×C8 | C2×D191 | semidirect |
| 176. C22⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133234 | 2 |
| #27133227 | 2 |
| #27133005 | 2 |
| #27132988 | 2 |
| #27132909 | 2 |
| #27132892 | 2 |
| #27132816 | 2 |
| #27132804 | 2 |
| #408×C191 | 2 |
| #3200 | 191 |