Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012106 | C2 | semidirect |
| 2. #26011895 | C2 | semidirect |
| 3. #26011874 | C2 | semidirect |
| 4. #26011849 | C2 | semidirect |
| 5. #26011736 | C2 | semidirect |
| 6. #26011733 | C2 | semidirect |
| 8. #26011591 | C2 | semidirect |
| 9. C4×Dic692 | C2 | semidirect |
| 10. #26011445 | C2 | semidirect |
| 11. C4×D8×C173 | C2 | semidirect |
| 117. C173 | #3175 | semidirect |
| 128. C4×D8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012106 | 2 |
| #26011895 | 2 |
| #26011874 | 2 |
| #26011849 | 2 |
| #26011736 | 2 |
| #26011733 | 2 |
| #26011724 | 2 |
| #26011591 | 2 |
| C4×Dic692 | 2 |
| #26011445 | 2 |
| C4×D8×C173 | 2 |
| #3175 | 173 |