Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C7×#2141 | C2 | semidirect |
| 4. #11729821 | C2 | semidirect |
| 6. #11725618 | C2 | semidirect |
| 7. #11725532 | C2 | semidirect |
| 17. #89951 | C4 | semidirect |
| 36. C2×C7×Q16 | C2×C4 | semidirect |
| 68. #6386 | C2×C4 | semidirect |
| 75. #2141 | D7 | semidirect |
| 196. C2×Q16 | C4×D7 | semidirect |
| 332. C7 | #13026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89951 | 2 |
| #11736611 | 2 |
| C7×#2141 | 2 |
| #11729821 | 2 |
| C2×#89313 | 2 |
| #11725618 | 2 |
| #11725532 | 2 |
| #13026 | 7 |