Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| 4. #26011254 | C2 | semidirect |
| 5. #336×C173 | C2 | semidirect |
| 24. C2×D692 | Q8 | semidirect |
| 96. C173 | #2023 | semidirect |
| 102. #336 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| C2×#19149601 | 2 |
| #26011393 | 2 |
| #26011254 | 2 |
| #336×C173 | 2 |
| #2023 | 173 |