Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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×D4×Q8 | C2 | semidirect |
| 2. #90268 | C2 | semidirect |
| 3. #89860 | C2 | semidirect |
| 4. #89859 | C2 | semidirect |
| 5. Q8×C7⋊C8 | C2 | semidirect |
| 6. #89787 | C2 | semidirect |
| 7. C4×#1141 | C2 | semidirect |
| 46. D4×Q8 | D7 | semidirect |
| 55. C7×Q8 | D8 | semidirect |
| 57. C7×D4 | #41 | semidirect |
| 128. Q8 | #1141 | semidirect |
| 134. D4 | #1161 | semidirect |
| 144. C7 | #3358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Q8 | 2 |
| #90268 | 2 |
| #89860 | 2 |
| #89859 | 2 |
| Q8×C7⋊C8 | 2 |
| #89787 | 2 |
| C4×#1141 | 2 |
| #3358 | 7 |