Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #26011965 | C2 | semidirect |
| 3. #26011507 | C2 | semidirect |
| 4. #26011497 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011248 | C2 | semidirect |
| 7. #344×C173 | C2 | semidirect |
| 12. C2×#14583815 | C4 | semidirect |
| 13. C2×D1384 | C4 | semidirect |
| 30. C2×Dic346 | C2×C4 | semidirect |
| 35. C2×D692 | C2×C4 | semidirect |
| 56. C2×C8×C173 | C2×C4 | semidirect |
| 115. C173 | #1904 | semidirect |
| 122. #344 | D173 | semidirect |
| 165. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26011965 | 2 |
| #26011507 | 2 |
| #26011497 | 2 |
| #26011464 | 2 |
| #26011248 | 2 |
| #344×C173 | 2 |
| #1904 | 173 |