Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. #26012096 | C2 | semidirect |
| 2. #26011890 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011857 | C2 | semidirect |
| 5. #26011855 | C2 | semidirect |
| 6. #26011742 | C2 | semidirect |
| 7. #26011725 | C2 | semidirect |
| 8. #26011601 | C2 | semidirect |
| 9. C4×#14583811 | C2 | semidirect |
| 10. #26011447 | C2 | semidirect |
| 11. #540×C173 | C2 | semidirect |
| 114. C173 | #3176 | semidirect |
| 117. #540 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012096 | 2 |
| #26011890 | 2 |
| #26011867 | 2 |
| #26011857 | 2 |
| #26011855 | 2 |
| #26011742 | 2 |
| #26011725 | 2 |
| #26011601 | 2 |
| C4×#14583811 | 2 |
| #26011447 | 2 |
| #540×C173 | 2 |
| #3176 | 173 |