Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133213 | C2 | semidirect |
| 2. #27133073 | C2 | semidirect |
| 3. #27133053 | C2 | semidirect |
| 4. #27133029 | C2 | semidirect |
| 5. #27133022 | C2 | semidirect |
| 6. #27132914 | C2 | semidirect |
| 7. #27132911 | C2 | semidirect |
| 8. C4×#15690274 | C2 | semidirect |
| 9. C4×#15690272 | C2 | semidirect |
| 10. C4×#15690271 | C2 | semidirect |
| 11. #529×C191 | C2 | semidirect |
| 92. C191⋊C8 | #41 | semidirect |
| 137. C191 | #3171 | semidirect |
| 140. #529 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| #27133073 | 2 |
| #27133053 | 2 |
| #27133029 | 2 |
| #27133022 | 2 |
| #27132914 | 2 |
| #27132911 | 2 |
| C4×#15690274 | 2 |
| C4×#15690272 | 2 |
| C4×#15690271 | 2 |
| #529×C191 | 2 |
| #3171 | 191 |