Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
576 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 213 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. #26011394 | C2 | semidirect |
| 2. #26011384 | C2 | semidirect |
| 3. #26011377 | C2 | semidirect |
| 4. #26011371 | C2 | semidirect |
| 5. #26011371 | C2 | semidirect |
| 6. #26011366 | C2 | semidirect |
| 7. #26011354 | C2 | semidirect |
| 8. #26011351 | C2 | semidirect |
| 29. #121×C173 | C4 | semidirect |
| 54. C2×D4×C173 | C2×C4 | semidirect |
| 56. C22×C4×C173 | C2×C4 | semidirect |
| 60. C4⋊C4×C173 | C2×C4 | semidirect |
| 61. C22⋊C4×C173 | C2×C4 | semidirect |
| 129. C173 | #2377 | semidirect |
| 144. #121 | Dic173 | semidirect |
| 168. C2×D4 | C2×Dic173 | semidirect |
| 177. C22×C4 | C2×Dic173 | semidirect |
| 183. C4⋊C4 | C2×Dic173 | semidirect |
| 190. C22⋊C4 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011394 | 2 |
| #26011384 | 2 |
| #26011377 | 2 |
| #26011371 | 2 |
| #26011366 | 2 |
| #26011354 | 2 |
| #26011351 | 2 |
| C2×#121×C173 | 2 |
| #2377 | 173 |