Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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×#2254 | C2 | semidirect |
| 3. #11729138 | C2 | semidirect |
| 5. #11727097 | C2 | semidirect |
| 7. #11726800 | C2 | semidirect |
| 48. D7×C16 | Q8 | semidirect |
| 51. #2254 | D7 | semidirect |
| 187. C7 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739383 | 2 |
| C7×#2254 | 2 |
| #11729138 | 2 |
| #11727099 | 2 |
| #11727097 | 2 |
| C4×D7×C16 | 2 |
| #11726800 | 2 |
| #33726 | 7 |