Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
600 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 309 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. #26011390 | C2 | semidirect |
| 13. C2×C4⋊C4×C173 | C4 | semidirect |
| 40. C2×C4×C173 | C4⋊C4 | semidirect |
| 64. C173 | #2316 | semidirect |
| 75. C2×C4⋊C4 | Dic173 | semidirect |
| 105. C2×C4 | C4⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149638 | 2 |
| #26011390 | 2 |
| #26011351 | 2 |
| C22×C4⋊C4×C173 | 2 |
| #2316 | 173 |