Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
374 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 35. #10587536 | C8 | semidirect |
| 36. #10587535 | C8 | semidirect |
| 43. C17×#108 | C8 | semidirect |
| 44. #10587493 | C8 | semidirect |
| 45. #10587490 | C8 | semidirect |
| 87. #3633 | #108 | direct (N × H) |
| 151. #108 | #3633 | direct (N × H) |
| 166. C17 | C8×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545908 | 2 |
| M16×#3633 | 2 |
| C2×C8×#3633 | 2 |
| #14545791 | 2 |
| #108×#595 | 2 |
| C8×#108 | 17 |