Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
354 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 188 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. #14543696 | C2 | semidirect |
| 3. C8×#63216 | C2 | semidirect |
| 20. #10587530 | C8 | direct (N × H) |
| 46. #63216 | C2×C8 | semidirect |
| 60. C8×C17 | M32 | semidirect |
| 62. #3622 | M32 | semidirect |
| 107. C17 | C8×M32 | semidirect |
| 139. C8 | #10587530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587530 | 2 |
| #14543696 | 2 |
| C8×#63216 | 2 |
| C82×D17 | 2 |
| C8×M32 | 17 |