Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#20259330 | C2 | semidirect |
| 2. C22×#15690270 | C2 | semidirect |
| 4. #27132740 | C2 | semidirect |
| 5. #27132733 | C2 | semidirect |
| 6. #27132629 | C2 | semidirect |
| 7. #27132626 | C2 | semidirect |
| 8. #27132619 | C2 | semidirect |
| 9. #424×C191 | C2 | semidirect |
| 17. C2×#15690270 | C22 | semidirect |
| 19. C2×C8×D191 | C22 | semidirect |
| 26. (C2×D191)⋊C8 | C22 | semidirect |
| 27. #20259233 | C22 | semidirect |
| 28. C4×C191⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C191 | C22 | semidirect |
| 50. C2×C191⋊C8 | D4 | semidirect |
| 113. C191 | #2930 | semidirect |
| 120. #424 | D191 | semidirect |
| 142. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259330 | 2 |
| C22×#15690270 | 2 |
| #27133175 | 2 |
| #27132740 | 2 |
| #27132733 | 2 |
| #27132629 | 2 |
| #27132626 | 2 |
| #27132619 | 2 |
| #424×C191 | 2 |
| #2930 | 191 |