Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26011795 | C2 | semidirect |
| 3. #26011783 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 35. C2×Dic346 | Q8 | semidirect |
| 106. C173 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011795 | 2 |
| #26011783 | 2 |
| #26011773 | 2 |
| #26011534 | 2 |
| #26011515 | 2 |
| #26011499 | 2 |
| #533×C173 | 2 |
| #3078 | 173 |