Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#90000 | C2 | semidirect |
| 4. C7×#1446 | C2 | semidirect |
| 5. C2×#89247 | C2 | semidirect |
| 7. #11725419 | C2 | semidirect |
| 85. #1446 | D7 | semidirect |
| 452. C7 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90000 | 2 |
| C2×#89999 | 2 |
| #11730824 | 2 |
| C7×#1446 | 2 |
| C2×#89247 | 2 |
| C2×#89246 | 2 |
| #11725419 | 2 |
| #9965 | 7 |