Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #27133220 | C2 | semidirect |
| 2. #27133073 | C2 | semidirect |
| 3. #27133058 | C2 | semidirect |
| 4. #27133033 | C2 | semidirect |
| 5. #27133022 | C2 | semidirect |
| 6. #27132919 | C2 | semidirect |
| 8. C4×#15690277 | C2 | semidirect |
| 9. C4×#15690275 | C2 | semidirect |
| 10. C4×#15690271 | C2 | semidirect |
| 129. C191 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133073 | 2 |
| #27133058 | 2 |
| #27133033 | 2 |
| #27133022 | 2 |
| #27132919 | 2 |
| #27132907 | 2 |
| C4×#15690277 | 2 |
| C4×#15690275 | 2 |
| C4×#15690271 | 2 |
| #529×C191 | 2 |
| #3172 | 191 |