Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #26012535 | C2 | semidirect |
| 2. #26012419 | C2 | semidirect |
| 3. #26012406 | C2 | semidirect |
| 4. C16×#10621924 | C2 | semidirect |
| 12. #19149622 | C4 | semidirect |
| 13. D2768 | C4 | semidirect |
| 15. Q32×C173 | C4 | semidirect |
| 49. C173 | #2178 | semidirect |
| 58. Q32 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012535 | 2 |
| #26012419 | 2 |
| #26012406 | 2 |
| C16×#10621924 | 2 |
| #26011924 | 2 |
| #2178 | 173 |