Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×Dic7⋊C8 | C2 | semidirect |
| 5. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 6. C7×#336 | C2 | semidirect |
| 7. #89345 | C2 | semidirect |
| 64. #336 | D7 | semidirect |
| 78. C2×C4×C7 | M16 | semidirect |
| 93. C2×Dic7 | M16 | semidirect |
| 208. C2×C4 | #1131 | semidirect |
| 219. C7 | #1851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1131 | 2 |
| C2×(C2×D7)⋊C8 | 2 |
| C2×Dic7⋊C8 | 2 |
| C4×(C2×D7)⋊C4 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C7×#336 | 2 |
| #89345 | 2 |
| #1851 | 7 |