Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #26011387 | C2 | semidirect |
| 5. #26011253 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. C2×#106×C173 | C2 | semidirect |
| 17. #19149601 | C4 | semidirect |
| 41. C4⋊Dic173 | C2×C4 | semidirect |
| 51. C2×C8×C173 | C2×C4 | semidirect |
| 66. D692 | C4⋊C4 | semidirect |
| 123. C173 | #1864 | semidirect |
| 126. C2×#106 | D173 | semidirect |
| 169. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149641 | 2 |
| C2×#19149601 | 2 |
| C2×#19149599 | 2 |
| #26011387 | 2 |
| #26011253 | 2 |
| #26011245 | 2 |
| C2×#106×C173 | 2 |
| #1864 | 173 |