Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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×#1706 | C2 | semidirect |
| 2. #11729136 | C2 | semidirect |
| 3. #11729135 | C2 | semidirect |
| 4. #11729045 | C2 | semidirect |
| 6. #11725814 | C2 | semidirect |
| 7. #11725244 | C2 | semidirect |
| 52. #1706 | D7 | semidirect |
| 206. C7 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1706 | 2 |
| #11729136 | 2 |
| #11729135 | 2 |
| #11729045 | 2 |
| #11729044 | 2 |
| #11725814 | 2 |
| #11725244 | 2 |
| #12527 | 7 |