Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 410 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. #27133214 | C2 | semidirect |
| 2. #27133198 | C2 | semidirect |
| 3. #27133052 | C2 | semidirect |
| 4. #27133029 | C2 | semidirect |
| 5. #27133025 | C2 | semidirect |
| 6. #27132900 | C2 | semidirect |
| 7. #27132893 | C2 | semidirect |
| 8. #27132774 | C2 | semidirect |
| 9. #27132762 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #501×C191 | C2 | semidirect |
| 110. C8×C191 | #41 | semidirect |
| 137. C191 | #3180 | semidirect |
| 141. #501 | D191 | semidirect |
| 248. C8 | #15690288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133214 | 2 |
| #27133198 | 2 |
| #27133052 | 2 |
| #27133029 | 2 |
| #27133025 | 2 |
| #27132900 | 2 |
| #27132893 | 2 |
| #27132774 | 2 |
| #27132762 | 2 |
| #97×D191 | 2 |
| #501×C191 | 2 |
| #3180 | 191 |