Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 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. #26011837 | C2 | semidirect |
| 2. #26011782 | C2 | semidirect |
| 4. #26011556 | C2 | semidirect |
| 5. #26011241 | C2 | semidirect |
| 6. #26011239 | C2 | semidirect |
| 7. #331×C173 | C2 | semidirect |
| 82. C173 | #1677 | semidirect |
| 90. #331 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011837 | 2 |
| #26011782 | 2 |
| #26011683 | 2 |
| #26011556 | 2 |
| #26011241 | 2 |
| #26011239 | 2 |
| #331×C173 | 2 |
| #1677 | 173 |