Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #27133194 | C2 | semidirect |
| 2. #27132969 | C2 | semidirect |
| 3. #27132961 | C2 | semidirect |
| 4. #27132904 | C2 | semidirect |
| 5. #27132890 | C2 | semidirect |
| 6. #27132884 | C2 | semidirect |
| 7. #27132876 | C2 | semidirect |
| 8. C2×Dic191⋊C8 | C2 | semidirect |
| 106. C191 | #3250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133194 | 2 |
| #27132969 | 2 |
| #27132961 | 2 |
| #27132904 | 2 |
| #27132890 | 2 |
| #27132884 | 2 |
| #27132876 | 2 |
| C2×Dic191⋊C8 | 2 |
| #466×C191 | 2 |
| #3250 | 191 |