Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#6399 | C2 | semidirect |
| 3. #89905 | C2 | semidirect |
| 4. #89748 | C2 | semidirect |
| 5. C7×#343 | C2 | semidirect |
| 41. C4×Dic7 | D4 | semidirect |
| 46. #343 | D7 | semidirect |
| 150. C7 | #2039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90201 | 2 |
| C2×#6399 | 2 |
| #89905 | 2 |
| #89748 | 2 |
| C7×#343 | 2 |
| #2039 | 7 |