Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133294 | C2 | semidirect |
| 3. #27133026 | C2 | semidirect |
| 4. #27133021 | C2 | semidirect |
| 5. #27133016 | C2 | semidirect |
| 6. #27133008 | C2 | semidirect |
| 7. #27132668 | C2 | semidirect |
| 8. #27132662 | C2 | semidirect |
| 9. #27132660 | C2 | semidirect |
| 10. #27132618 | C2 | semidirect |
| 11. C2×#102×C191 | C2 | semidirect |
| 15. #20259321 | C22 | semidirect |
| 18. #20259313 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259245 | C22 | semidirect |
| 29. #20259244 | C22 | semidirect |
| 30. #20259244 | C22 | semidirect |
| 33. #20259242 | C22 | semidirect |
| 34. #20259232 | C22 | semidirect |
| 35. C8×Dic191 | C22 | semidirect |
| 135. C191 | #3136 | semidirect |
| 146. C2×#102 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133294 | 2 |
| #27133230 | 2 |
| #27133026 | 2 |
| #27133021 | 2 |
| #27133016 | 2 |
| #27133008 | 2 |
| #27132668 | 2 |
| #27132662 | 2 |
| #27132660 | 2 |
| #27132618 | 2 |
| C2×#102×C191 | 2 |
| #3136 | 191 |