Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 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×C4×C7×D4 | C2 | semidirect |
| 3. C2×#6406 | C2 | semidirect |
| 4. C2×#6383 | C2 | semidirect |
| 5. #89711 | C2 | semidirect |
| 6. #89324 | C2 | semidirect |
| 7. #89319 | C2 | semidirect |
| 18. C2×#1141 | C4 | semidirect |
| 48. C2×D28 | C2×C4 | semidirect |
| 64. C2×C7⋊C8 | C2×C4 | semidirect |
| 66. C2×C4×D4 | D7 | semidirect |
| 90. C7×D4 | C22⋊C4 | semidirect |
| 100. C2×C4×C7 | D8 | semidirect |
| 232. D4 | (C2×D7)⋊C4 | semidirect |
| 245. C2×C4 | #1141 | semidirect |
| 254. C7 | #1879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C22×#1141 | 2 |
| C2×#6406 | 2 |
| C2×#6383 | 2 |
| #89711 | 2 |
| #89324 | 2 |
| #89319 | 2 |
| #1879 | 7 |