Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
288 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 111. C7×Q8 | Q32 | semidirect |
| 210. Q8 | #6403 | semidirect |
| 225. C7 | #12358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic28 | 2 |
| C7×#1670 | 2 |
| #11729070 | 2 |
| #11729064 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725282 | 2 |
| #11725278 | 2 |
| #12358 | 7 |