Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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. #26011896 | C2 | semidirect |
| 3. #26011871 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 6. C4×Dic692 | C2 | semidirect |
| 52. C2×C4×C173 | Q16 | semidirect |
| 77. C173 | #3170 | semidirect |
| 130. C2×C4 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011896 | 2 |
| #26011871 | 2 |
| #26011842 | 2 |
| #26011732 | 2 |
| C4×Dic692 | 2 |
| C2×C4×C8×C173 | 2 |
| #3170 | 173 |