Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
698 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 698 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. #14545926 | C2 | semidirect |
| 2. #14545918 | C2 | semidirect |
| 3. C2×D4⋊#3633 | C2 | semidirect |
| 35. C4×#3633 | D4 | semidirect |
| 36. C17×#127 | C8 | semidirect |
| 38. #10587626 | C8 | semidirect |
| 39. #10587560 | C8 | semidirect |
| 165. #127 | #3633 | semidirect |
| 181. C17 | #9642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545926 | 2 |
| #14545918 | 2 |
| C2×D4⋊#3633 | 2 |
| #127×#595 | 2 |
| #9642 | 17 |