Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #26011266 | C2 | semidirect |
| 5. C4×#14583801 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. #346×C173 | C2 | semidirect |
| 11. #19149618 | C4 | semidirect |
| 14. C16×D173 | C4 | semidirect |
| 60. C173 | #2108 | semidirect |
| 66. #346 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149618 | 2 |
| C2×C16×D173 | 2 |
| #26011445 | 2 |
| #26011266 | 2 |
| C4×#14583801 | 2 |
| C16×Dic173 | 2 |
| #346×C173 | 2 |
| #2108 | 173 |