Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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×#19149698 | C2 | semidirect |
| 2. #26012039 | C2 | semidirect |
| 3. C4×#14583825 | C2 | semidirect |
| 4. #26011712 | C2 | semidirect |
| 5. #26011704 | C2 | semidirect |
| 6. #26011702 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011688 | C2 | semidirect |
| 9. C4⋊C8×D173 | C2 | semidirect |
| 10. #26011484 | C2 | semidirect |
| 11. #459×C173 | C2 | semidirect |
| 47. #14583825 | D4 | semidirect |
| 135. C4×C173 | #135 | semidirect |
| 150. C173 | #3035 | semidirect |
| 160. #459 | D173 | semidirect |
| 292. C4 | #19149698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149698 | 2 |
| #26012039 | 2 |
| C4×#14583825 | 2 |
| #26011712 | 2 |
| #26011704 | 2 |
| #26011702 | 2 |
| #26011696 | 2 |
| #26011688 | 2 |
| C4⋊C8×D173 | 2 |
| #26011484 | 2 |
| #459×C173 | 2 |
| #3035 | 173 |