Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11727516 | C2 | semidirect |
| 4. C7×#1277 | C2 | semidirect |
| 5. #11725508 | C2 | semidirect |
| 39. #1277 | D7 | semidirect |
| 212. C7 | #10621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728233 | 2 |
| #11727541 | 2 |
| #11727516 | 2 |
| C7×#1277 | 2 |
| #11725508 | 2 |
| #10621 | 7 |