Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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×#1591 | C2 | semidirect |
| 4. #11725571 | C2 | semidirect |
| 6. #11725276 | C2 | semidirect |
| 7. C8×C7⋊C16 | C2 | semidirect |
| 46. #1591 | D7 | semidirect |
| 75. C7⋊C16 | M16 | semidirect |
| 108. C7×C8 | SD32 | semidirect |
| 191. C8 | #6402 | semidirect |
| 194. C7 | #12082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1591 | 2 |
| C4×#6402 | 2 |
| #11725806 | 2 |
| #11725571 | 2 |
| #11725277 | 2 |
| #11725276 | 2 |
| C8×C7⋊C16 | 2 |
| #12082 | 7 |