Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3249 | C2 | semidirect |
| 4. #11729595 | C2 | semidirect |
| 5. #11729589 | C2 | semidirect |
| 7. #11725512 | C2 | semidirect |
| 77. #3249 | D7 | semidirect |
| 362. C7 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3249 | 2 |
| #11740800 | 2 |
| #11740781 | 2 |
| #11729595 | 2 |
| #11729589 | 2 |
| #11728211 | 2 |
| #11725512 | 2 |
| #10195 | 7 |