Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26012357 | C2 | semidirect |
| 6. C2×#14583835 | C4 | semidirect |
| 17. C2×#13063443 | C2×C4 | semidirect |
| 42. C2×Dic173 | M16 | semidirect |
| 56. C2×C4×C173 | M16 | semidirect |
| 78. C173 | #1728 | semidirect |
| 134. C2×C4 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583835 | 2 |
| #26012357 | 2 |
| C22×C4×Dic173 | 2 |
| #1728 | 173 |