Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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. #27133218 | C2 | semidirect |
| 3. #27133057 | C2 | semidirect |
| 4. #27133033 | C2 | semidirect |
| 5. #27133025 | C2 | semidirect |
| 6. #27132905 | C2 | semidirect |
| 8. #27132769 | C2 | semidirect |
| 9. #27132762 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #501×C191 | C2 | semidirect |
| 129. C191 | #3181 | semidirect |
| 133. #501 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133198 | 2 |
| #27133057 | 2 |
| #27133033 | 2 |
| #27133025 | 2 |
| #27132905 | 2 |
| #27132893 | 2 |
| #27132769 | 2 |
| #27132762 | 2 |
| #97×D191 | 2 |
| #501×C191 | 2 |
| #3181 | 191 |