Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26011901 | C2 | semidirect |
| 3. #26011894 | C2 | semidirect |
| 4. #26011887 | C2 | semidirect |
| 33. #14583810 | Q8 | semidirect |
| 60. #13063436 | C2×Q8 | semidirect |
| 92. C173 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| #26011901 | 2 |
| #26011894 | 2 |
| #26011887 | 2 |
| #26011534 | 2 |
| C4×#14583810 | 2 |
| #533×C173 | 2 |
| #3165 | 173 |