Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
210 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 108. C7⋊C8 | Q32 | semidirect |
| 185. C7 | #12083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6403 | 2 |
| #11728659 | 2 |
| #11726318 | 2 |
| C7×#1332 | 2 |
| #11725311 | 2 |
| C16×C7⋊C8 | 2 |
| #11725275 | 2 |
| #12083 | 7 |