Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #14545784 | C2 | semidirect |
| 4. #14545784 | C2 | semidirect |
| 46. C17×#117 | C8 | semidirect |
| 47. #10587612 | C8 | semidirect |
| 48. #10587578 | C8 | semidirect |
| 49. #10587578 | C8 | semidirect |
| 104. C4⋊C4×C17 | C2×C8 | semidirect |
| 105. C4⋊C4×C17 | C2×C8 | semidirect |
| 111. C4⋊Dic17 | C2×C8 | semidirect |
| 112. C4⋊Dic17 | C2×C8 | semidirect |
| 249. #117 | #3633 | semidirect |
| 272. C17 | #7579 | semidirect |
| 315. C4⋊C4 | C2×#3633 | semidirect |
| 316. C4⋊C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545925 | 2 |
| C2×(C2×#3633)⋊C4 | 2 |
| #14545784 | 2 |
| #14545244 | 2 |
| #7579 | 17 |