Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 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. #26012516 | C2 | semidirect |
| 2. #26012515 | C2 | semidirect |
| 3. #26012496 | C2 | semidirect |
| 4. #26012495 | C2 | semidirect |
| 6. C4×#14583836 | C2 | semidirect |
| 10. #19149746 | C22 | semidirect |
| 11. C4⋊#13063443 | C22 | semidirect |
| 14. #19149734 | C22 | semidirect |
| 15. C4×#13063443 | C22 | semidirect |
| 104. C173 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012516 | 2 |
| #26012515 | 2 |
| #26012496 | 2 |
| #26012495 | 2 |
| #26012462 | 2 |
| C4×#14583836 | 2 |
| #117×D173 | 2 |
| #2921 | 173 |