Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
182 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26011865 | C2 | semidirect |
| 2. #26011768 | C2 | semidirect |
| 4. #26011568 | C2 | semidirect |
| 5. #26011243 | C2 | semidirect |
| 6. #26011234 | C2 | semidirect |
| 7. #332×C173 | C2 | semidirect |
| 57. #13063436 | D8 | semidirect |
| 85. C173 | #1685 | semidirect |
| 92. #332 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011865 | 2 |
| #26011768 | 2 |
| #26011687 | 2 |
| #26011568 | 2 |
| #26011243 | 2 |
| #26011234 | 2 |
| #332×C173 | 2 |
| #1685 | 173 |