Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1998 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1998 conjugacy classes of subgroups — too many to draw. Only its 491 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 |
|---|---|---|
| 4. #11729323 | C2 | semidirect |
| 8. C22×C7×C4⋊C4 | C4 | semidirect |
| 63. C22×C4⋊C4 | Dic7 | semidirect |
| 182. C7 | #14342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C4⋊C4 | 2 |
| C2×#89983 | 2 |
| #11729881 | 2 |
| #11729323 | 2 |
| #14342 | 7 |