Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 75 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×#2240 | C2 | semidirect |
| 2. #11729135 | C2 | semidirect |
| 3. #11729115 | C2 | semidirect |
| 4. #11729042 | C2 | semidirect |
| 6. #11726812 | C2 | semidirect |
| 7. #11725304 | C2 | semidirect |
| 48. #2240 | D7 | semidirect |
| 198. C7 | #12513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2240 | 2 |
| #11729135 | 2 |
| #11729115 | 2 |
| #11729042 | 2 |
| #11729030 | 2 |
| #11726812 | 2 |
| #11725304 | 2 |
| #12513 | 7 |