Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 5. C7×C4⋊Q8 | C4 | semidirect |
| 6. C7×C4⋊Q8 | C4 | semidirect |
| 7. C7×#125 | C4 | semidirect |
| 42. #1136 | Q8 | semidirect |
| 68. C4⋊Q8 | Dic7 | semidirect |
| 69. C4⋊Q8 | Dic7 | semidirect |
| 70. #125 | Dic7 | semidirect |
| 143. C7 | #1986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| C4×C4⋊Dic7 | 2 |
| C4×#1136 | 2 |
| #89327 | 2 |
| #1986 | 7 |