Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. #26011777 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 7. #26011599 | C2 | semidirect |
| 103. C173 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×C4×Dic346 | 2 |
| #26011822 | 2 |
| #26011777 | 2 |
| #26011702 | 2 |
| #26011649 | 2 |
| #26011599 | 2 |
| #432×C173 | 2 |
| #3113 | 173 |