Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#10587489 | C2 | semidirect |
| 4. #11762572 | C2 | semidirect |
| 15. C17×C22⋊C8 | C4 | semidirect |
| 33. C2×C8×C17 | C2×C4 | semidirect |
| 75. C22×C17 | #107 | semidirect |
| 112. C22⋊C8 | Dic17 | semidirect |
| 114. C17 | #1852 | semidirect |
| 130. C2×C8 | C2×Dic17 | semidirect |
| 171. C22 | #10587489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic17 | 2 |
| C2×#10587489 | 2 |
| #11762669 | 2 |
| #11762572 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1852 | 17 |