Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. C2×#6384 | C2 | semidirect |
| 5. #89701 | C2 | semidirect |
| 6. #89324 | C2 | semidirect |
| 7. #89319 | C2 | semidirect |
| 18. C2×#1142 | C4 | semidirect |
| 48. C2×Dic14 | C2×C4 | semidirect |
| 62. C2×C7⋊C8 | C2×C4 | semidirect |
| 91. C2×C4×C7 | SD16 | semidirect |
| 226. C2×C4 | #1142 | semidirect |
| 235. C7 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C22×#1142 | 2 |
| C2×#6406 | 2 |
| C2×#6384 | 2 |
| #89701 | 2 |
| #89324 | 2 |
| #89319 | 2 |
| #1877 | 7 |