Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133275 | C2 | semidirect |
| 3. #27133005 | C2 | semidirect |
| 4. #27132964 | C2 | semidirect |
| 5. #27132869 | C2 | semidirect |
| 7. #27132765 | C2 | semidirect |
| 8. C4×#15690276 | C2 | semidirect |
| 9. #433×C191 | C2 | semidirect |
| 13. #20259322 | C22 | semidirect |
| 15. #20259314 | C22 | semidirect |
| 18. C4×Dic382 | C22 | semidirect |
| 24. #20259256 | C22 | semidirect |
| 25. #20259254 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 31. C4⋊C8×C191 | C22 | semidirect |
| 33. #97×C191 | C22 | semidirect |
| 34. C4×C8×C191 | C22 | semidirect |
| 102. C191 | #3123 | semidirect |
| 112. #433 | D191 | semidirect |
| 130. C4⋊C8 | C2×D191 | semidirect |
| 136. #97 | C2×D191 | semidirect |
| 137. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133275 | 2 |
| #27133137 | 2 |
| #27133005 | 2 |
| #27132964 | 2 |
| #27132869 | 2 |
| #27132816 | 2 |
| #27132765 | 2 |
| C4×#15690276 | 2 |
| #433×C191 | 2 |
| #3123 | 191 |