Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 166 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. #26011870 | C2 | semidirect |
| 5. #26011241 | C2 | semidirect |
| 6. #26011238 | C2 | semidirect |
| 7. #332×C173 | C2 | semidirect |
| 78. C173 | #1689 | semidirect |
| 86. #332 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011870 | 2 |
| #26011772 | 2 |
| #26011768 | 2 |
| #26011568 | 2 |
| #26011241 | 2 |
| #26011238 | 2 |
| #332×C173 | 2 |
| #1689 | 173 |