Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19149708 | C2 | semidirect |
| 3. C4×Q8×D173 | C2 | semidirect |
| 4. #26011712 | C2 | semidirect |
| 5. #26011711 | C2 | semidirect |
| 6. #26011702 | C2 | semidirect |
| 7. #26011701 | C2 | semidirect |
| 8. #26011688 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 10. #26011489 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 50. Q8×D173 | D4 | semidirect |
| 132. C4×C173 | #137 | semidirect |
| 146. C173 | #3037 | semidirect |
| 156. #460 | D173 | semidirect |
| 285. C4 | #19149708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149708 | 2 |
| #26012039 | 2 |
| C4×Q8×D173 | 2 |
| #26011712 | 2 |
| #26011711 | 2 |
| #26011702 | 2 |
| #26011701 | 2 |
| #26011688 | 2 |
| #26011513 | 2 |
| #26011489 | 2 |
| #460×C173 | 2 |
| #3037 | 173 |