Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
534 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C22×C7×Q32 | C2 | semidirect |
| 4. #11729823 | C2 | semidirect |
| 5. C2×#89360 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 82. C22×Q32 | D7 | semidirect |
| 371. C7 | #13339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q32 | 2 |
| #11741326 | 2 |
| C2×#89951 | 2 |
| #11729823 | 2 |
| C2×#89360 | 2 |
| C2×#89305 | 2 |
| #11725611 | 2 |
| #13339 | 7 |