Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#6392 | C2 | semidirect |
| 3. C2×#6386 | C2 | semidirect |
| 4. #89359 | C2 | semidirect |
| 5. #89357 | C2 | semidirect |
| 8. C7×#135 | C4 | semidirect |
| 28. C7×Q16 | C2×C4 | semidirect |
| 31. C7×D8 | C2×C4 | semidirect |
| 64. #135 | Dic7 | semidirect |
| 95. Q16 | C2×Dic7 | semidirect |
| 98. D8 | C2×Dic7 | semidirect |
| 129. C7 | #2139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#135 | 2 |
| C2×#6392 | 2 |
| C2×#6386 | 2 |
| #89359 | 2 |
| #89357 | 2 |
| #2139 | 7 |