Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. M16×Dic7 | C2 | semidirect |
| 5. C42×Dic7 | C2 | semidirect |
| 6. #89350 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 11. Q8×Dic7 | C4 | semidirect |
| 13. D4×Dic7 | C4 | semidirect |
| 21. C7×#104 | C4 | semidirect |
| 22. #6411 | C4 | semidirect |
| 40. C7×M16 | C2×C4 | semidirect |
| 43. C42×C7 | C2×C4 | semidirect |
| 53. C4×Dic7 | C2×C4 | semidirect |
| 57. #1136 | C2×C4 | semidirect |
| 69. C7×Q8 | C42 | semidirect |
| 73. C7×D4 | C42 | semidirect |
| 108. #104 | Dic7 | direct (N × H) |
| 126. Dic7 | #104 | direct (N × H) |
| 143. M16 | C2×Dic7 | semidirect |
| 159. C42 | C2×Dic7 | semidirect |
| 168. Q8 | C4×Dic7 | semidirect |
| 172. D4 | C4×Dic7 | semidirect |
| 193. C7 | C4×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic7 | 2 |
| C2×C7×#104 | 2 |
| C2×#6411 | 2 |
| M16×Dic7 | 2 |
| C42×Dic7 | 2 |
| #89350 | 2 |
| #89318 | 2 |
| C4×#104 | 7 |