Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 6. C7×#500 | C4 | semidirect |
| 7. C7×#494 | C4 | semidirect |
| 12. C4×C7×Q16 | C4 | semidirect |
| 82. #500 | Dic7 | semidirect |
| 83. #494 | Dic7 | semidirect |
| 88. C4×Q16 | Dic7 | semidirect |
| 216. C7 | #11745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3170 | 2 |
| C4×#6391 | 2 |
| #11727499 | 2 |
| #11725582 | 2 |
| #11745 | 7 |