Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #27132736 | C2 | semidirect |
| 3. #27132733 | C2 | semidirect |
| 4. C8×D764 | C2 | semidirect |
| 5. #27132728 | C2 | semidirect |
| 6. #27132724 | C2 | semidirect |
| 7. #27132628 | C2 | semidirect |
| 8. C22⋊C8×D191 | C2 | semidirect |
| 9. #433×C191 | C2 | semidirect |
| 12. C2×#15690270 | C22 | semidirect |
| 15. C2×C8×D191 | C22 | semidirect |
| 22. C4⋊(C191⋊C8) | C22 | semidirect |
| 26. (C2×D191)⋊C8 | C22 | semidirect |
| 27. (C2×D191)⋊C8 | C22 | semidirect |
| 28. #20259233 | C22 | semidirect |
| 29. C4×C191⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C191 | C22 | semidirect |
| 33. #97×C191 | C22 | semidirect |
| 34. C4×C8×C191 | C22 | semidirect |
| 114. C191 | #2977 | semidirect |
| 122. #433 | D191 | semidirect |
| 139. C4⋊C8 | C2×D191 | semidirect |
| 147. #97 | C2×D191 | semidirect |
| 149. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133175 | 2 |
| #27132736 | 2 |
| #27132733 | 2 |
| C8×D764 | 2 |
| #27132728 | 2 |
| #27132724 | 2 |
| #27132628 | 2 |
| C22⋊C8×D191 | 2 |
| #433×C191 | 2 |
| #2977 | 191 |