Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 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. #27133211 | C2 | semidirect |
| 2. #27133192 | C2 | semidirect |
| 3. #27133072 | C2 | semidirect |
| 4. #27133027 | C2 | semidirect |
| 5. #27133022 | C2 | semidirect |
| 6. #27132913 | C2 | semidirect |
| 7. #27132906 | C2 | semidirect |
| 8. SD16×Dic191 | C2 | semidirect |
| 9. D8×Dic191 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #496×C191 | C2 | semidirect |
| 110. C8×C191 | #41 | semidirect |
| 137. C191 | #3171 | semidirect |
| 142. #496 | D191 | semidirect |
| 248. C8 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| #27133192 | 2 |
| #27133072 | 2 |
| #27133027 | 2 |
| #27133022 | 2 |
| #27132913 | 2 |
| #27132906 | 2 |
| SD16×Dic191 | 2 |
| D8×Dic191 | 2 |
| #27132615 | 2 |
| #496×C191 | 2 |
| #3171 | 191 |