Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C2×#89474 | C2 | semidirect |
| 4. C2×#89260 | C2 | semidirect |
| 6. #11727306 | C2 | semidirect |
| 7. C7×#1295 | C2 | semidirect |
| 83. #1295 | D7 | semidirect |
| 355. C7 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89486 | 2 |
| C2×#89474 | 2 |
| #11731700 | 2 |
| C2×#89260 | 2 |
| C2×#89259 | 2 |
| #11727306 | 2 |
| C7×#1295 | 2 |
| #10086 | 7 |