Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #27133005 | C2 | semidirect |
| 4. #27133005 | C2 | semidirect |
| 5. #27132999 | C2 | semidirect |
| 6. #27132994 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. #27132701 | C2 | semidirect |
| 9. #27132673 | C2 | semidirect |
| 10. C2×#20259247 | C2 | semidirect |
| 126. C191 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133234 | 2 |
| #27133146 | 2 |
| #27133005 | 2 |
| #27132999 | 2 |
| #27132994 | 2 |
| #27132705 | 2 |
| #27132701 | 2 |
| #27132673 | 2 |
| C2×#20259247 | 2 |
| #408×C191 | 2 |
| #3097 | 191 |