Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×C7×#494 | C2 | semidirect |
| 3. C2×#89856 | C2 | semidirect |
| 4. C2×#89341 | C2 | semidirect |
| 5. #11729058 | C2 | direct (N × H) |
| 6. C2×#89254 | C2 | semidirect |
| 18. C7×#494 | C22 | semidirect |
| 21. #89856 | C22 | semidirect |
| 25. #89341 | C22 | semidirect |
| 26. #89254 | C22 | semidirect |
| 67. C2×#494 | D7 | semidirect |
| 123. #494 | C2×D7 | semidirect |
| 256. C2×C7 | #1634 | semidirect |
| 291. C7 | C2×#1634 | semidirect |
| 308. C2 | #11729058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90425 | 2 |
| C2×C7×#494 | 2 |
| C2×#89856 | 2 |
| C2×#89341 | 2 |
| #11729058 | 2 |
| C2×#89254 | 2 |
| C2×#1634 | 7 |