Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×#19149734 | C2 | semidirect |
| 4. #26012357 | C2 | semidirect |
| 7. C2×D173⋊C8 | C4 | semidirect |
| 11. #19149736 | C4 | semidirect |
| 40. #13063443 | C22⋊C4 | semidirect |
| 71. C2×D173 | #97 | semidirect |
| 84. C173 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| C2×#19149736 | 2 |
| C2×#19149734 | 2 |
| #26012357 | 2 |
| #26011338 | 2 |
| #1752 | 173 |