Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
176 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 73 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. C8×Dic346 | C2 | semidirect |
| 4. #26011244 | C2 | semidirect |
| 5. #26011223 | C2 | semidirect |
| 7. #322×C173 | C2 | semidirect |
| 26. #14583815 | C8 | semidirect |
| 43. Dic346 | C2×C8 | semidirect |
| 60. C8×C173 | C2×C8 | semidirect |
| 77. C173 | SD16⋊C8 | semidirect |
| 85. #322 | D173 | semidirect |
| 138. C8 | C8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic346 | 2 |
| C4×#14583815 | 2 |
| C8×D692 | 2 |
| #26011244 | 2 |
| #26011223 | 2 |
| #26011220 | 2 |
| #322×C173 | 2 |
| SD16⋊C8 | 173 |