Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#20259353 | C2 | semidirect |
| 3. C2×#20259353 | C2 | semidirect |
| 4. #27133429 | C2 | semidirect |
| 5. #27132937 | C2 | semidirect |
| 6. #27132929 | C2 | semidirect |
| 7. #27132711 | C2 | semidirect |
| 8. #27132645 | C2 | semidirect |
| 9. C2×#101×C191 | C2 | semidirect |
| 22. C2×#15690277 | C22 | semidirect |
| 24. C2×#15690274 | C22 | semidirect |
| 30. #20259257 | C22 | semidirect |
| 31. #20259240 | C22 | semidirect |
| 32. #20259238 | C22 | semidirect |
| 36. #101×C191 | C22 | semidirect |
| 142. C191 | #3069 | semidirect |
| 152. C2×#101 | D191 | semidirect |
| 178. #101 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| C2×#20259353 | 2 |
| #27133429 | 2 |
| #27132937 | 2 |
| #27132929 | 2 |
| #27132711 | 2 |
| #27132645 | 2 |
| C2×#101×C191 | 2 |
| #3069 | 191 |