Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 210 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. #26012498 | C2 | semidirect |
| 4. #26012497 | C2 | semidirect |
| 5. D173⋊(C4⋊C8) | C2 | semidirect |
| 15. #19149746 | C22 | semidirect |
| 16. C4⋊#13063443 | C22 | semidirect |
| 95. D173 | #424 | semidirect |
| 96. C173 | C2×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊M16 | 2 |
| C22×D173⋊C8 | 2 |
| #26012498 | 2 |
| #26012497 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #117×D173 | 2 |
| C2×#424 | 173 |