Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
194 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C7×#1397 | C2 | semidirect |
| 4. Dic7⋊C32 | C2 | semidirect |
| 5. #11725314 | C2 | semidirect |
| 35. #1397 | D7 | semidirect |
| 143. C7 | #13640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D7×C16 | 2 |
| C7×#1397 | 2 |
| (C2×D7)⋊C32 | 2 |
| Dic7⋊C32 | 2 |
| #11725314 | 2 |
| #13640 | 7 |