Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3229 | C2 | semidirect |
| 4. #11729592 | C2 | semidirect |
| 5. #11729540 | C2 | semidirect |
| 7. #11725547 | C2 | semidirect |
| 77. #3229 | D7 | semidirect |
| 337. C7 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3229 | 2 |
| #11740780 | 2 |
| #11740660 | 2 |
| #11729592 | 2 |
| #11729540 | 2 |
| #11728544 | 2 |
| #11725547 | 2 |
| #10226 | 7 |