Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
366 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27133220 | C2 | semidirect |
| 3. #27133072 | C2 | semidirect |
| 4. #27133057 | C2 | semidirect |
| 5. #27133032 | C2 | semidirect |
| 6. #27133023 | C2 | semidirect |
| 7. #27132904 | C2 | semidirect |
| 9. #27132771 | C2 | semidirect |
| 10. #27132765 | C2 | semidirect |
| 11. C2×#97×C191 | C2 | semidirect |
| 129. C191 | #3181 | semidirect |
| 141. C2×#97 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133197 | 2 |
| #27133072 | 2 |
| #27133057 | 2 |
| #27133032 | 2 |
| #27133023 | 2 |
| #27132904 | 2 |
| #27132892 | 2 |
| #27132771 | 2 |
| #27132765 | 2 |
| C2×#97×C191 | 2 |
| #3181 | 191 |