Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #90213 | C2 | semidirect |
| 3. C7×#427 | C2 | semidirect |
| 4. C2×C8×Dic7 | C2 | semidirect |
| 5. #89774 | C2 | semidirect |
| 6. #89645 | C2 | semidirect |
| 7. #89644 | C2 | semidirect |
| 8. #89624 | C2 | semidirect |
| 15. #6467 | C4 | semidirect |
| 34. #1157 | C2×C4 | semidirect |
| 39. C2×C7×C8 | C2×C4 | semidirect |
| 53. Dic28 | C2×C4 | semidirect |
| 54. D56 | C2×C4 | semidirect |
| 55. #1132 | C2×C4 | semidirect |
| 61. #427 | D7 | semidirect |
| 116. Dic7 | #135 | semidirect |
| 131. C2×C8 | C4×D7 | semidirect |
| 168. C7 | C4×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6467 | 2 |
| #90213 | 2 |
| C7×#427 | 2 |
| C2×C8×Dic7 | 2 |
| #89774 | 2 |
| #89645 | 2 |
| #89644 | 2 |
| #89624 | 2 |
| C4×#135 | 7 |