Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 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. #26011867 | C2 | semidirect |
| 2. #26011687 | C2 | semidirect |
| 3. #26011683 | C2 | semidirect |
| 4. #26011568 | C2 | semidirect |
| 5. #26011241 | C2 | semidirect |
| 6. #26011234 | C2 | semidirect |
| 7. #331×C173 | C2 | semidirect |
| 58. #13063436 | D8 | semidirect |
| 92. C173 | #1687 | semidirect |
| 100. #331 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011867 | 2 |
| #26011687 | 2 |
| #26011683 | 2 |
| #26011568 | 2 |
| #26011241 | 2 |
| #26011234 | 2 |
| #331×C173 | 2 |
| #1687 | 173 |