Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26012558 | C2 | semidirect |
| 2. C2×#19149738 | C2 | semidirect |
| 3. D173⋊#99 | C2 | semidirect |
| 4. #26012368 | C2 | semidirect |
| 17. #19149662 | C4 | semidirect |
| 21. #19149649 | C4 | semidirect |
| 22. #19149647 | C4 | semidirect |
| 24. #123×C173 | C4 | semidirect |
| 33. C22⋊#10621924 | D4 | semidirect |
| 35. C23×D173 | C2×C4 | semidirect |
| 52. C22⋊Dic173 | C2×C4 | semidirect |
| 58. C22×C4×C173 | C2×C4 | semidirect |
| 61. C22⋊C4×C173 | C2×C4 | semidirect |
| 135. C173 | #1913 | semidirect |
| 146. #123 | #10621924 | semidirect |
| 181. C22×C4 | C2×#10621924 | semidirect |
| 196. C22⋊C4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012558 | 2 |
| C2×#19149738 | 2 |
| D173⋊#99 | 2 |
| #26012368 | 2 |
| #26012052 | 2 |
| #1913 | 173 |