Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #26012462 | C2 | semidirect |
| 2. C2×(C2×#10621924)⋊C4 | C2 | semidirect |
| 3. #26012344 | C2 | semidirect |
| 4. #26012342 | C2 | semidirect |
| 12. C2×#14583825 | C4 | semidirect |
| 16. #19149658 | C4 | semidirect |
| 21. #19149637 | C4 | semidirect |
| 22. #121×C173 | C4 | semidirect |
| 31. C2×Dic346 | C2×C4 | semidirect |
| 42. C4⋊Dic173 | C2×C4 | semidirect |
| 50. C2×D4×C173 | C2×C4 | semidirect |
| 52. C4⋊C4×C173 | C2×C4 | semidirect |
| 119. C173 | #1504 | semidirect |
| 134. #121 | #10621924 | semidirect |
| 149. C2×D4 | C2×#10621924 | semidirect |
| 167. C4⋊C4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012462 | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| #26012344 | 2 |
| #26012342 | 2 |
| #26012001 | 2 |
| #1504 | 173 |