Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4×C22⋊#3633 | C2 | semidirect |
| 2. C2×(C2×#3633)⋊C4 | C2 | semidirect |
| 3. #14545784 | C2 | semidirect |
| 4. #14545783 | C2 | semidirect |
| 52. C17×#121 | C8 | semidirect |
| 54. #10587624 | C8 | semidirect |
| 55. #10587616 | C8 | semidirect |
| 56. #10587581 | C8 | semidirect |
| 89. C2×D4×C17 | C2×C8 | semidirect |
| 100. C2×D68 | C2×C8 | semidirect |
| 122. C4⋊C4×C17 | C2×C8 | semidirect |
| 127. C4⋊Dic17 | C2×C8 | semidirect |
| 284. #121 | #3633 | semidirect |
| 308. C17 | #7565 | semidirect |
| 321. C2×D4 | C2×#3633 | semidirect |
| 360. C4⋊C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#3633 | 2 |
| C2×(C2×#3633)⋊C4 | 2 |
| #14545784 | 2 |
| #14545783 | 2 |
| #121×#595 | 2 |
| #7565 | 17 |