Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 1. C2×C4×Dic346 | C2 | semidirect |
| 2. #26011802 | C2 | semidirect |
| 3. #26011783 | C2 | semidirect |
| 4. #26011688 | C2 | semidirect |
| 5. #26011629 | C2 | semidirect |
| 6. #26011591 | C2 | semidirect |
| 7. #26011548 | C2 | semidirect |
| 66. Dic346 | #41 | semidirect |
| 111. C173 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011802 | 2 |
| #26011783 | 2 |
| #26011688 | 2 |
| #26011629 | 2 |
| #26011591 | 2 |
| #26011548 | 2 |
| #532×C173 | 2 |
| #3112 | 173 |