Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#6551 | C2 | semidirect |
| 2. C2×#6510 | C2 | semidirect |
| 3. C2×#6471 | C2 | semidirect |
| 4. C2×C7×#101 | C2 | semidirect |
| 5. C2×#6399 | C2 | semidirect |
| 6. #89525 | C2 | direct (N × H) |
| 10. #6551 | C22 | semidirect |
| 18. #6510 | C22 | semidirect |
| 22. #6471 | C22 | semidirect |
| 25. C7×#101 | C22 | semidirect |
| 26. #6399 | C22 | semidirect |
| 70. C2×#101 | D7 | semidirect |
| 122. #101 | C2×D7 | semidirect |
| 177. C2×C7 | #454 | semidirect |
| 213. C7 | C2×#454 | semidirect |
| 233. C2 | #89525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6551 | 2 |
| C2×#6510 | 2 |
| C2×#6471 | 2 |
| C2×C7×#101 | 2 |
| C2×#6399 | 2 |
| #89525 | 2 |
| C2×#454 | 7 |