Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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×#410 | C2 | semidirect |
| 4. C2×#6411 | C2 | semidirect |
| 5. #89777 | C2 | semidirect |
| 6. #89328 | C2 | semidirect |
| 7. #89327 | C2 | semidirect |
| 15. #6505 | C4 | semidirect |
| 16. #6495 | C4 | semidirect |
| 34. C2×C7×Q8 | C2×C4 | semidirect |
| 36. C2×C7×D4 | C2×C4 | semidirect |
| 68. #1136 | C2×C4 | semidirect |
| 75. #410 | D7 | semidirect |
| 161. C2×Q8 | C4×D7 | semidirect |
| 165. C2×D4 | C4×D7 | semidirect |
| 234. C7 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90513 | 2 |
| #90213 | 2 |
| C7×#410 | 2 |
| C2×#6411 | 2 |
| #89777 | 2 |
| #89328 | 2 |
| #89327 | 2 |
| #1906 | 7 |