Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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×C8×Dic7 | C2 | semidirect |
| 5. C2×#6377 | C2 | semidirect |
| 6. C7×#336 | C2 | semidirect |
| 7. #89345 | C2 | semidirect |
| 18. C2×#1131 | C4 | semidirect |
| 20. (C2×D7)⋊C8 | C4 | semidirect |
| 59. #336 | D7 | semidirect |
| 80. C2×Dic7 | M16 | semidirect |
| 88. C7⋊C8 | C22⋊C4 | semidirect |
| 185. C7 | #1753 | 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×C8×Dic7 | 2 |
| C4×(C2×D7)⋊C4 | 2 |
| C2×#6377 | 2 |
| C7×#336 | 2 |
| #89345 | 2 |
| #1753 | 7 |