Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011529 | C2 | semidirect |
| 3. #26011507 | C2 | semidirect |
| 4. #26011464 | C2 | semidirect |
| 5. #405×C173 | C2 | semidirect |
| 11. C2×Dic692 | C4 | semidirect |
| 12. C2×#14583815 | C4 | semidirect |
| 13. C2×D1384 | C4 | semidirect |
| 96. C173 | #1976 | semidirect |
| 102. #405 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26011529 | 2 |
| #26011507 | 2 |
| #26011464 | 2 |
| #405×C173 | 2 |
| #1976 | 173 |