Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 198 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. #26012506 | C2 | semidirect |
| 3. C2×#19149750 | C2 | semidirect |
| 4. D173⋊#108 | C2 | semidirect |
| 73. C173 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012570 | 2 |
| #26012506 | 2 |
| C2×#19149750 | 2 |
| D173⋊#108 | 2 |
| #131×D173 | 2 |
| #2916 | 173 |