Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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×#2216 | C2 | semidirect |
| 2. C2×#89316 | C2 | semidirect |
| 4. C2×#89294 | C2 | semidirect |
| 5. #11725632 | C2 | semidirect |
| 6. #11725383 | C2 | semidirect |
| 7. #11725381 | C2 | semidirect |
| 40. C7⋊C32 | D4 | semidirect |
| 43. #2216 | D7 | semidirect |
| 172. C7 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2216 | 2 |
| C2×#89316 | 2 |
| #11729167 | 2 |
| C2×#89294 | 2 |
| #11725632 | 2 |
| #11725383 | 2 |
| #11725381 | 2 |
| #13699 | 7 |