Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27133192 | C2 | semidirect |
| 3. #27133069 | C2 | semidirect |
| 4. #27133053 | C2 | semidirect |
| 5. #27133028 | C2 | semidirect |
| 6. #27132915 | C2 | semidirect |
| 7. #27132912 | C2 | semidirect |
| 8. #27132748 | C2 | semidirect |
| 9. #27132743 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #489×C191 | C2 | semidirect |
| 100. C191⋊C8 | #41 | semidirect |
| 137. C191 | #3171 | semidirect |
| 144. #489 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133214 | 2 |
| #27133192 | 2 |
| #27133069 | 2 |
| #27133053 | 2 |
| #27133028 | 2 |
| #27132915 | 2 |
| #27132912 | 2 |
| #27132748 | 2 |
| #27132743 | 2 |
| #27132615 | 2 |
| #489×C191 | 2 |
| #3171 | 191 |