Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133064 | C2 | semidirect |
| 3. #27133046 | C2 | semidirect |
| 4. #27133016 | C2 | semidirect |
| 5. #27132904 | C2 | semidirect |
| 6. #27132890 | C2 | semidirect |
| 7. #27132757 | C2 | semidirect |
| 8. #27132754 | C2 | semidirect |
| 9. D8×Dic191 | C2 | semidirect |
| 10. C2×C8×Dic191 | C2 | semidirect |
| 118. C191 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133194 | 2 |
| #27133064 | 2 |
| #27133046 | 2 |
| #27133016 | 2 |
| #27132904 | 2 |
| #27132890 | 2 |
| #27132757 | 2 |
| #27132754 | 2 |
| D8×Dic191 | 2 |
| C2×C8×Dic191 | 2 |
| #466×C191 | 2 |
| #3168 | 191 |