Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 13. #10587630 | C4 | semidirect |
| 112. Dic17 | #103 | semidirect |
| 145. C17 | #1981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587630 | 2 |
| C2×#10587485 | 2 |
| C2×#10587487 | 2 |
| C2×#10587506 | 2 |
| C2×#10587481 | 2 |
| C4⋊C4×Dic17 | 2 |
| C2×C17×#103 | 2 |
| #1981 | 17 |