Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×D4×Dic173 | C2 | semidirect |
| 2. C2×#19149600 | C2 | semidirect |
| 3. C2×#19149600 | C2 | semidirect |
| 4. #26011394 | C2 | semidirect |
| 5. #26011254 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 24. C2×D8×C173 | C4 | semidirect |
| 56. C2×D4×C173 | C2×C4 | semidirect |
| 63. C2×C8×C173 | C2×C4 | semidirect |
| 76. C2×Dic173 | D8 | semidirect |
| 100. D4×C173 | C22⋊C4 | semidirect |
| 146. C173 | #1879 | semidirect |
| 160. C2×D8 | Dic173 | semidirect |
| 184. C2×D4 | C2×Dic173 | semidirect |
| 201. C2×C8 | C2×Dic173 | semidirect |
| 233. D4 | C22⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic173 | 2 |
| C2×#19149600 | 2 |
| #26011394 | 2 |
| #26011254 | 2 |
| #26011245 | 2 |
| C22×D8×C173 | 2 |
| #1879 | 173 |