Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 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. #27133210 | C2 | semidirect |
| 2. #27133060 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133008 | C2 | semidirect |
| 5. #27132917 | C2 | semidirect |
| 6. #27132915 | C2 | semidirect |
| 7. #27132913 | C2 | semidirect |
| 8. #27132776 | C2 | semidirect |
| 9. #27132773 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #442×C191 | C2 | semidirect |
| 87. C191⋊C8 | #41 | semidirect |
| 96. C8×C191 | #41 | semidirect |
| 118. C191 | #3184 | semidirect |
| 129. #442 | D191 | semidirect |
| 215. C8 | #15690287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133210 | 2 |
| #27133060 | 2 |
| #27133038 | 2 |
| #27133008 | 2 |
| #27132917 | 2 |
| #27132915 | 2 |
| #27132913 | 2 |
| #27132776 | 2 |
| #27132773 | 2 |
| #27132615 | 2 |
| #442×C191 | 2 |
| #3184 | 191 |