Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×C7×Q16 | C2 | semidirect |
| 3. C2×#6403 | C2 | semidirect |
| 4. #89951 | C2 | direct (N × H) |
| 5. C2×#6402 | C2 | semidirect |
| 6. C2×#6386 | C2 | semidirect |
| 12. C2×C7×Q16 | C22 | semidirect |
| 19. #6403 | C22 | semidirect |
| 20. #6402 | C22 | semidirect |
| 21. #6386 | C22 | semidirect |
| 50. C22×Q16 | D7 | semidirect |
| 84. C2×Q16 | C2×D7 | semidirect |
| 128. C2×C7 | #510 | semidirect |
| 152. C7 | C2×#510 | semidirect |
| 165. C2 | #89951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| C2×#6467 | 2 |
| C2×#6403 | 2 |
| #89951 | 2 |
| C2×#6402 | 2 |
| C2×#6386 | 2 |
| C2×#510 | 7 |