Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #11728507 | C2 | semidirect |
| 5. #11725542 | C2 | semidirect |
| 15. C7×#333 | C4 | semidirect |
| 16. C7×#333 | C4 | semidirect |
| 17. C7×#331 | C4 | semidirect |
| 87. #333 | Dic7 | semidirect |
| 88. #333 | Dic7 | semidirect |
| 89. #331 | Dic7 | semidirect |
| 207. C7 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740723 | 2 |
| C7×#1543 | 2 |
| #11729569 | 2 |
| #11728507 | 2 |
| #11725542 | 2 |
| #8935 | 7 |