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. #27133024 | C2 | semidirect |
| 5. #27133019 | C2 | semidirect |
| 6. #27133008 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. C2×#20259242 | C2 | semidirect |
| 10. #27132621 | C2 | semidirect |
| 11. #417×C191 | C2 | semidirect |
| 15. #20259321 | C22 | semidirect |
| 18. #20259313 | C22 | semidirect |
| 26. #20259246 | C22 | semidirect |
| 27. #20259246 | C22 | semidirect |
| 30. #20259243 | C22 | semidirect |
| 31. #20259243 | C22 | semidirect |
| 34. #20259232 | C22 | semidirect |
| 35. C8×Dic191 | C22 | semidirect |
| 39. #103×C191 | C22 | semidirect |
| 40. #102×C191 | C22 | semidirect |
| 135. C191 | #3136 | semidirect |
| 144. #417 | D191 | semidirect |
| 167. #103 | C2×D191 | semidirect |
| 174. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133294 | 2 |
| #27133227 | 2 |
| #27133026 | 2 |
| #27133024 | 2 |
| #27133019 | 2 |
| #27133008 | 2 |
| #27132669 | 2 |
| #27132659 | 2 |
| C2×#20259242 | 2 |
| #27132621 | 2 |
| #417×C191 | 2 |
| #3136 | 191 |