Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 48. #6432 | Q8 | semidirect |
| 333. C7 | #10359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731663 | 2 |
| #11727582 | 2 |
| #11727576 | 2 |
| #11727309 | 2 |
| C7×#1295 | 2 |
| #11725465 | 2 |
| #10359 | 7 |