Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
406 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #11725594 | C2 | semidirect |
| 6. C2×C7×C4⋊Q8 | C4 | semidirect |
| 8. C7×#494 | C4 | semidirect |
| 10. C4×C7×M16 | C4 | semidirect |
| 70. C2×C4⋊Q8 | Dic7 | semidirect |
| 72. #494 | Dic7 | semidirect |
| 75. C4×M16 | Dic7 | semidirect |
| 188. C7 | #13586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3152 | 2 |
| #11729573 | 2 |
| #11725594 | 2 |
| #13586 | 7 |