Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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. #11762693 | C2 | semidirect |
| 3. #11762691 | C2 | semidirect |
| 14. C2×#63225 | C4 | semidirect |
| 107. C17 | #2313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63225 | 2 |
| #11762693 | 2 |
| #11762691 | 2 |
| #11762670 | 2 |
| #11762667 | 2 |
| C4×C22⋊Dic17 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2313 | 17 |