Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #26012515 | C2 | semidirect |
| 2. #26012514 | C2 | semidirect |
| 3. #26012510 | C2 | semidirect |
| 4. #26012498 | C2 | semidirect |
| 7. #26012456 | C2 | semidirect |
| 11. #19149746 | C22 | semidirect |
| 12. C4⋊#13063443 | C22 | semidirect |
| 18. #19149734 | C22 | semidirect |
| 19. C4×#13063443 | C22 | semidirect |
| 110. C173 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012515 | 2 |
| #26012514 | 2 |
| #26012510 | 2 |
| #26012498 | 2 |
| #26012462 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012456 | 2 |
| #117×D173 | 2 |
| #2924 | 173 |