Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11733626 | C2 | semidirect |
| 5. #11725444 | C2 | semidirect |
| 6. #11725286 | C2 | semidirect |
| 7. #11725284 | C2 | semidirect |
| 116. C4⋊Dic7 | SD16 | semidirect |
| 384. C7 | #7747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733626 | 2 |
| C7×#2041 | 2 |
| #11729522 | 2 |
| #11729516 | 2 |
| #11725444 | 2 |
| #11725286 | 2 |
| #11725284 | 2 |
| #7747 | 7 |