Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149700 | C2 | semidirect |
| 2. #26012161 | C2 | semidirect |
| 3. #26012144 | C2 | semidirect |
| 4. #26011717 | C2 | semidirect |
| 5. #26011698 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011650 | C2 | semidirect |
| 8. #26011635 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. C8×D692 | C2 | semidirect |
| 11. #492×C173 | C2 | semidirect |
| 57. #14583815 | D4 | semidirect |
| 127. C4×C173 | #135 | semidirect |
| 140. C173 | #3284 | semidirect |
| 145. #492 | D173 | semidirect |
| 272. C4 | #19149700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149700 | 2 |
| #26012161 | 2 |
| #26012144 | 2 |
| #26011717 | 2 |
| #26011698 | 2 |
| #26011683 | 2 |
| #26011650 | 2 |
| #26011635 | 2 |
| C4×#14583815 | 2 |
| C8×D692 | 2 |
| #492×C173 | 2 |
| #3284 | 173 |