Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15690275 | C2 | semidirect |
| 2. C2×#20259330 | C2 | semidirect |
| 3. #27133239 | C2 | semidirect |
| 5. #27132908 | C2 | semidirect |
| 6. #27132891 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132673 | C2 | semidirect |
| 9. #418×C191 | C2 | semidirect |
| 16. C2×#15690270 | C22 | semidirect |
| 18. C2×C8×D191 | C22 | semidirect |
| 24. #20259302 | C22 | semidirect |
| 28. #20259255 | C22 | semidirect |
| 29. #20259253 | C22 | semidirect |
| 30. #20259247 | C22 | semidirect |
| 50. C2×C191⋊C8 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
| 130. #418 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| C2×#20259330 | 2 |
| #27133239 | 2 |
| #27133230 | 2 |
| #27132908 | 2 |
| #27132891 | 2 |
| #27132699 | 2 |
| #27132673 | 2 |
| #418×C191 | 2 |
| #3057 | 191 |