Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
378 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 378 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. C7×#3164 | C2 | semidirect |
| 5. #11725530 | C2 | semidirect |
| 6. #11725529 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 43. C2×D56 | Q8 | semidirect |
| 64. #3164 | D7 | semidirect |
| 291. C7 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3164 | 2 |
| #11728406 | 2 |
| C2×#89286 | 2 |
| #11727657 | 2 |
| #11725530 | 2 |
| #11725529 | 2 |
| #11725477 | 2 |
| #13369 | 7 |