Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 10. C4×#3624 | C4 | semidirect |
| 21. C4×Dic17 | C8 | semidirect |
| 64. C17 | #1744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#3624 | 2 |
| #11763675 | 2 |
| C42×Dic17 | 2 |
| #1744 | 17 |