Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #26012455 | C2 | semidirect |
| 4. #26012372 | C2 | semidirect |
| 8. C2×#14583836 | C4 | semidirect |
| 9. C2×#14583835 | C4 | semidirect |
| 12. C2×D173⋊C8 | C4 | semidirect |
| 13. C22×#13063443 | C4 | semidirect |
| 15. #19149740 | C4 | semidirect |
| 16. #19149739 | C4 | semidirect |
| 97. C173 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149766 | 2 |
| #26012478 | 2 |
| #26012455 | 2 |
| #26012372 | 2 |
| #26011463 | 2 |
| #1757 | 173 |