Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
418 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 10. #11763700 | C4 | direct (N × H) |
| 11. #11763698 | C4 | semidirect |
| 12. C4×#63216 | C4 | semidirect |
| 15. #11762584 | C4 | semidirect |
| 16. C4×#63214 | C4 | semidirect |
| 17. C4×C16×C17 | C4 | semidirect |
| 54. #63216 | C42 | semidirect |
| 55. C16×C17 | C42 | semidirect |
| 56. #63214 | C42 | semidirect |
| 81. C4×C17 | #347 | semidirect |
| 98. C4×C16 | #595 | semidirect |
| 120. C17 | C4×#347 | semidirect |
| 141. C16 | C4×#595 | semidirect |
| 163. C4 | #11763700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763700 | 2 |
| C4×#10587530 | 2 |
| C4×#10587532 | 2 |
| C4×#10587469 | 2 |
| C4×#347 | 17 |