Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11739460 | C2 | semidirect |
| 2. #11737340 | C2 | semidirect |
| 3. C7×#2170 | C2 | semidirect |
| 4. #11729210 | C2 | semidirect |
| 5. #11727060 | C2 | semidirect |
| 6. #11726883 | C2 | semidirect |
| 7. #11726821 | C2 | semidirect |
| 8. #11726820 | C2 | semidirect |
| 74. #2170 | D7 | semidirect |
| 263. C7 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739460 | 2 |
| #11737340 | 2 |
| C7×#2170 | 2 |
| #11729210 | 2 |
| #11727060 | 2 |
| #11726883 | 2 |
| #11726821 | 2 |
| #11726820 | 2 |
| #33860 | 7 |