Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14545792 | C2 | semidirect |
| 43. C2×C4⋊C4×C17 | C8 | semidirect |
| 44. C2×C4⋊Dic17 | C8 | semidirect |
| 48. C4⋊C4×D17 | C8 | semidirect |
| 228. C2×C4⋊C4 | #3633 | semidirect |
| 244. C17 | #8706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545924 | 2 |
| C4×C22⋊#3633 | 2 |
| #14545792 | 2 |
| C2×C4⋊C4×#595 | 2 |
| #8706 | 17 |