Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133291 | C2 | semidirect |
| 2. #27133031 | C2 | semidirect |
| 3. #27133022 | C2 | semidirect |
| 4. #27133017 | C2 | semidirect |
| 5. #27133013 | C2 | semidirect |
| 6. #27132672 | C2 | semidirect |
| 9. C2×#20259246 | C2 | semidirect |
| 10. #27132619 | C2 | semidirect |
| 127. C191 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133031 | 2 |
| #27133022 | 2 |
| #27133017 | 2 |
| #27133013 | 2 |
| #27132672 | 2 |
| #27132664 | 2 |
| #27132659 | 2 |
| C2×#20259246 | 2 |
| #27132619 | 2 |
| #536×C191 | 2 |
| #3137 | 191 |