Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012206 | C2 | semidirect |
| 2. #26012145 | C2 | semidirect |
| 3. #26011842 | C2 | semidirect |
| 4. #26011834 | C2 | semidirect |
| 5. #26011781 | C2 | semidirect |
| 6. #26011719 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011633 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #26011484 | C2 | semidirect |
| 11. C4×D8×C173 | C2 | semidirect |
| 130. C173 | #3303 | semidirect |
| 140. C4×D8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012206 | 2 |
| #26012145 | 2 |
| #26011842 | 2 |
| #26011834 | 2 |
| #26011781 | 2 |
| #26011719 | 2 |
| #26011696 | 2 |
| #26011633 | 2 |
| C8×D692 | 2 |
| #26011484 | 2 |
| C4×D8×C173 | 2 |
| #3303 | 173 |