Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133294 | C2 | semidirect |
| 3. #27133030 | C2 | semidirect |
| 4. #27133021 | C2 | semidirect |
| 5. #27133016 | C2 | semidirect |
| 6. #27133012 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 9. C2×#20259245 | C2 | semidirect |
| 10. #27132621 | 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 |
|---|---|
| #27133294 | 2 |
| #27133234 | 2 |
| #27133030 | 2 |
| #27133021 | 2 |
| #27133016 | 2 |
| #27133012 | 2 |
| #27132673 | 2 |
| #27132659 | 2 |
| C2×#20259245 | 2 |
| #27132621 | 2 |
| #417×C191 | 2 |
| #3137 | 191 |