Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1709 | C2 | semidirect |
| 2. #11729067 | C2 | semidirect |
| 3. #11729066 | C2 | semidirect |
| 4. #11729045 | C2 | semidirect |
| 6. #11725814 | C2 | semidirect |
| 7. C8×C7⋊C16 | C2 | semidirect |
| 49. #1709 | D7 | semidirect |
| 182. C7 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1709 | 2 |
| #11729067 | 2 |
| #11729066 | 2 |
| #11729045 | 2 |
| #11729044 | 2 |
| #11725814 | 2 |
| C8×C7⋊C16 | 2 |
| #12518 | 7 |