Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
222 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 19. C7×Q32 | C8 | semidirect |
| 76. Q32 | C7⋊C8 | semidirect |
| 126. C7 | #12044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×Q32 | 2 |
| Q16×C7⋊C8 | 2 |
| #11725571 | 2 |
| #11725307 | 2 |
| #11725304 | 2 |
| #12044 | 7 |