Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133030 | C2 | semidirect |
| 4. #27133026 | C2 | semidirect |
| 5. #27133025 | C2 | semidirect |
| 6. #27133023 | C2 | semidirect |
| 7. #27133022 | C2 | semidirect |
| 8. #27132658 | C2 | semidirect |
| 9. #27132656 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #489×C191 | C2 | semidirect |
| 137. C191 | #3135 | semidirect |
| 146. #489 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133212 | 2 |
| #27133030 | 2 |
| #27133026 | 2 |
| #27133025 | 2 |
| #27133023 | 2 |
| #27133022 | 2 |
| #27132658 | 2 |
| #27132656 | 2 |
| #97×D191 | 2 |
| #489×C191 | 2 |
| #3135 | 191 |