Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133291 | C2 | semidirect |
| 3. #27132964 | C2 | semidirect |
| 4. #27132964 | C2 | semidirect |
| 5. #27132954 | C2 | semidirect |
| 6. #27132944 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. #27132701 | C2 | semidirect |
| 11. #424×C191 | C2 | semidirect |
| 13. #20259322 | C22 | semidirect |
| 15. #20259314 | C22 | semidirect |
| 26. #20259256 | C22 | semidirect |
| 27. #20259256 | C22 | semidirect |
| 28. #20259256 | C22 | semidirect |
| 29. #20259254 | C22 | semidirect |
| 30. #20259254 | C22 | semidirect |
| 31. #20259254 | C22 | semidirect |
| 39. C4⋊C8×C191 | C22 | semidirect |
| 40. C4⋊C8×C191 | C22 | semidirect |
| 45. C2×D764 | Q8 | semidirect |
| 124. C191 | #3081 | semidirect |
| 134. #424 | D191 | semidirect |
| 160. C4⋊C8 | C2×D191 | semidirect |
| 161. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133137 | 2 |
| #27132964 | 2 |
| #27132954 | 2 |
| #27132944 | 2 |
| #27132705 | 2 |
| #27132701 | 2 |
| #27132669 | 2 |
| C2×#20259244 | 2 |
| #424×C191 | 2 |
| #3081 | 191 |