Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26012540 | C2 | semidirect |
| 3. #26012354 | C2 | semidirect |
| 4. #26012341 | C2 | semidirect |
| 6. #26012332 | C2 | semidirect |
| 32. #14583815 | C8 | semidirect |
| 48. Dic346 | C2×C8 | semidirect |
| 60. C8×C173 | C2×C8 | semidirect |
| 77. C173 | SD16⋊C8 | semidirect |
| 138. C8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012540 | 2 |
| #26012519 | 2 |
| #26012354 | 2 |
| #26012341 | 2 |
| #26012339 | 2 |
| #26012332 | 2 |
| #26011578 | 2 |
| SD16⋊C8 | 173 |