Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. #26011783 | C2 | semidirect |
| 3. #26011778 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 5. #26011768 | C2 | semidirect |
| 6. #26011531 | C2 | semidirect |
| 7. #26011515 | C2 | semidirect |
| 9. C2×C4⋊Q8×C173 | C2 | semidirect |
| 36. #14583826 | Q8 | semidirect |
| 72. Dic346 | C2×Q8 | semidirect |
| 74. D692 | C2×Q8 | semidirect |
| 121. C173 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| #26011783 | 2 |
| #26011778 | 2 |
| #26011773 | 2 |
| #26011768 | 2 |
| #26011531 | 2 |
| #26011515 | 2 |
| #26011490 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| #3079 | 173 |