Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
482 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 103 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×#2320 | C2 | semidirect |
| 3. #11729377 | C2 | semidirect |
| 6. #11725427 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 18. #89799 | C4 | semidirect |
| 20. #89793 | C4 | semidirect |
| 73. #2320 | D7 | semidirect |
| 334. C7 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2320 | 2 |
| #11739889 | 2 |
| #11729377 | 2 |
| #11727246 | 2 |
| #11727186 | 2 |
| #11725427 | 2 |
| #11725421 | 2 |
| #9330 | 7 |