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 |
|---|---|---|
| 1. C2×C7×#501 | C2 | semidirect |
| 4. #11729540 | C2 | semidirect |
| 5. C2×#89338 | C2 | semidirect |
| 7. #11725465 | C2 | semidirect |
| 77. C2×#501 | 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×C7×#501 | 2 |
| C2×#89861 | 2 |
| #11740516 | 2 |
| #11729540 | 2 |
| C2×#89338 | 2 |
| C2×#89259 | 2 |
| #11725465 | 2 |
| #10086 | 7 |