Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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. C7×#2255 | C2 | semidirect |
| 4. #11729134 | C2 | semidirect |
| 5. #11725605 | C2 | semidirect |
| 6. #11725324 | C2 | semidirect |
| 62. #2255 | D7 | semidirect |
| 248. C7 | #12412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739376 | 2 |
| C7×#2255 | 2 |
| #11729141 | 2 |
| #11729134 | 2 |
| #11725605 | 2 |
| #11725324 | 2 |
| #11725322 | 2 |
| #12412 | 7 |