Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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. #6450 | C4 | semidirect |
| 21. #6390 | C4 | semidirect |
| 23. #6384 | C4 | semidirect |
| 90. Dic14 | C42 | semidirect |
| 194. C7 | #1763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6450 | 2 |
| C2×#6390 | 2 |
| C2×#6389 | 2 |
| C4⋊C4×Dic7 | 2 |
| C2×#6384 | 2 |
| C7×#340 | 2 |
| #89324 | 2 |
| #1763 | 7 |