Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. C2×#19149733 | C2 | semidirect |
| 4. #26012442 | C2 | semidirect |
| 5. #26012365 | C2 | semidirect |
| 6. #26012364 | C2 | semidirect |
| 21. #19149601 | C4 | semidirect |
| 22. #19149600 | C4 | semidirect |
| 23. #19149599 | C4 | semidirect |
| 24. #102×C173 | C4 | semidirect |
| 134. C173 | #1936 | semidirect |
| 157. #102 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149741 | 2 |
| C2×#19149733 | 2 |
| #26012443 | 2 |
| #26012442 | 2 |
| #26012365 | 2 |
| #26012364 | 2 |
| #102×D173 | 2 |
| #1936 | 173 |