Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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. #26012332 | C2 | semidirect |
| 3. C8×#13063443 | C2 | semidirect |
| 20. C8×D173 | C8 | semidirect |
| 21. C8×D173 | C8 | semidirect |
| 51. C173 | #1450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012509 | 2 |
| #26012332 | 2 |
| C8×#13063443 | 2 |
| C4×C8×D173 | 2 |
| #1450 | 173 |