Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×#20259355 | C2 | semidirect |
| 3. #27133234 | C2 | semidirect |
| 4. #27133144 | C2 | semidirect |
| 5. #27132884 | C2 | semidirect |
| 6. #27132877 | C2 | semidirect |
| 7. #27132872 | C2 | semidirect |
| 8. #27132867 | C2 | semidirect |
| 9. #27132691 | C2 | semidirect |
| 10. C2×#20259245 | C2 | semidirect |
| 11. #417×C191 | C2 | semidirect |
| 146. C191 | #3046 | semidirect |
| 157. #417 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259342 | 2 |
| #27133234 | 2 |
| #27133144 | 2 |
| #27132884 | 2 |
| #27132877 | 2 |
| #27132872 | 2 |
| #27132867 | 2 |
| #27132691 | 2 |
| C2×#20259245 | 2 |
| #417×C191 | 2 |
| #3046 | 191 |