Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
330 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 120 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. #11763733 | C4 | direct (N × H) |
| 16. #11762584 | C4 | semidirect |
| 17. #11762584 | C4 | semidirect |
| 18. C4×#63214 | C4 | semidirect |
| 19. C4×C16×C17 | C4 | semidirect |
| 65. C16×C17 | C42 | semidirect |
| 67. #63214 | C42 | semidirect |
| 100. C4×C17 | #365 | semidirect |
| 117. C4×C16 | #595 | semidirect |
| 147. C17 | C4×#365 | semidirect |
| 172. C16 | C4×#595 | semidirect |
| 202. C4 | #11763733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763733 | 2 |
| C4×#10587535 | 2 |
| C4×#10587533 | 2 |
| #14543849 | 2 |
| C4×#10587469 | 2 |
| C4×#365 | 17 |