Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
528 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 206 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. #26012357 | C2 | semidirect |
| 6. C2×D173⋊C8 | C4 | semidirect |
| 17. C2×#13063443 | C2×C4 | semidirect |
| 23. C2×C4×D173 | C8 | semidirect |
| 41. C2×Dic173 | C2×C8 | semidirect |
| 55. C2×C4×C173 | C2×C8 | semidirect |
| 76. D173 | #336 | semidirect |
| 77. C173 | C2×#336 | semidirect |
| 132. C2×C4 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| #26012357 | 2 |
| C2×C42×D173 | 2 |
| C2×#336 | 173 |