Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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×#6372 | C2 | semidirect |
| 3. C4×C7×C16 | C2 | semidirect |
| 4. (C2×D7)⋊C16 | C2 | semidirect |
| 5. C4⋊(C7⋊C16) | C2 | semidirect |
| 27. C7×C16 | D4 | semidirect |
| 33. C4×C16 | D7 | semidirect |
| 60. C4×C7 | M32 | semidirect |
| 76. C16 | D28 | semidirect |
| 93. C7 | #2169 | semidirect |
| 100. C4 | #6372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6372 | 2 |
| C8×D28 | 2 |
| C4×C7×C16 | 2 |
| (C2×D7)⋊C16 | 2 |
| C4⋊(C7⋊C16) | 2 |
| #2169 | 7 |