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 |
|---|---|---|
| 1. C2×#19149679 | C2 | semidirect |
| 3. #26011787 | C2 | semidirect |
| 4. #26011782 | C2 | semidirect |
| 5. #26011777 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 7. #26011533 | C2 | semidirect |
| 9. #423×C173 | C2 | semidirect |
| 36. #14583826 | Q8 | semidirect |
| 74. Dic346 | C2×Q8 | semidirect |
| 76. D692 | C2×Q8 | semidirect |
| 121. C173 | #3079 | semidirect |
| 130. #423 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| C4×#14583826 | 2 |
| #26011787 | 2 |
| #26011782 | 2 |
| #26011777 | 2 |
| #26011772 | 2 |
| #26011533 | 2 |
| #26011493 | 2 |
| #423×C173 | 2 |
| #3079 | 173 |