Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 30. Dic56 | C8 | semidirect |
| 126. C7 | #12044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic56 | 2 |
| C8×Dic28 | 2 |
| C7×#1311 | 2 |
| #11725311 | 2 |
| #11725307 | 2 |
| #12044 | 7 |