Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 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×#20259313 | C2 | semidirect |
| 3. #27132973 | C2 | semidirect |
| 4. #27132969 | C2 | semidirect |
| 5. #27132966 | C2 | semidirect |
| 6. #27132962 | C2 | semidirect |
| 7. #27132706 | C2 | semidirect |
| 8. #27132686 | C2 | semidirect |
| 11. #428×C191 | C2 | semidirect |
| 135. C191 | #3080 | semidirect |
| 144. #428 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259313 | 2 |
| #27133131 | 2 |
| #27132973 | 2 |
| #27132969 | 2 |
| #27132966 | 2 |
| #27132962 | 2 |
| #27132706 | 2 |
| #27132686 | 2 |
| #27132665 | 2 |
| #27132662 | 2 |
| #428×C191 | 2 |
| #3080 | 191 |