Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. C7×C8×D4 | C2 | semidirect |
| 3. C8×D28 | C2 | semidirect |
| 4. D4⋊(C7⋊C8) | C2 | semidirect |
| 5. #89278 | C2 | semidirect |
| 6. #89274 | C2 | semidirect |
| 7. C8×C7⋊C8 | C2 | semidirect |
| 35. #1141 | C8 | direct (N × H) |
| 45. C8×D4 | D7 | semidirect |
| 53. C7×D4 | C2×C8 | semidirect |
| 62. D28 | C2×C8 | semidirect |
| 67. C7×C8 | D8 | semidirect |
| 71. C7⋊C8 | C2×C8 | semidirect |
| 130. D4 | C8×D7 | semidirect |
| 146. C8 | #1141 | direct (N × H) |
| 147. C7 | C8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D4 | 2 |
| C4×#1141 | 2 |
| C8×D28 | 2 |
| D4⋊(C7⋊C8) | 2 |
| #89278 | 2 |
| #89274 | 2 |
| C8×C7⋊C8 | 2 |
| C8×D8 | 7 |