Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
760 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 113 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×#89265 | C2 | semidirect |
| 3. #11727686 | C2 | semidirect |
| 4. #11727174 | C2 | semidirect |
| 5. C7×#1280 | C2 | semidirect |
| 55. C7⋊#95 | D4 | semidirect |
| 61. #1280 | D7 | semidirect |
| 409. C7 | #10402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11730826 | 2 |
| C2×#89265 | 2 |
| #11727686 | 2 |
| #11727174 | 2 |
| C7×#1280 | 2 |
| #10402 | 7 |