Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C2×#6374 | C2 | semidirect |
| 2. C4×Dic28 | C2 | semidirect |
| 4. C7×C4⋊C16 | C2 | semidirect |
| 5. #89304 | C2 | semidirect |
| 28. Dic28 | D4 | semidirect |
| 36. C4⋊C16 | D7 | semidirect |
| 68. C4×C7 | SD32 | semidirect |
| 108. C7 | #2207 | semidirect |
| 116. C4 | #6374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6374 | 2 |
| C4×Dic28 | 2 |
| #89467 | 2 |
| C7×C4⋊C16 | 2 |
| #89304 | 2 |
| #2207 | 7 |