Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 310 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. #26012068 | C2 | semidirect |
| 2. #26011627 | C2 | semidirect |
| 3. #26011624 | C2 | semidirect |
| 4. #26011409 | C2 | semidirect |
| 5. #26011224 | C2 | semidirect |
| 6. #26011216 | C2 | semidirect |
| 7. #327×C173 | C2 | semidirect |
| 85. C2×Dic173 | D8 | semidirect |
| 134. C173 | #1598 | semidirect |
| 141. #327 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012068 | 2 |
| #26011627 | 2 |
| #26011624 | 2 |
| #26011409 | 2 |
| #26011224 | 2 |
| #26011216 | 2 |
| #327×C173 | 2 |
| #1598 | 173 |