Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
574 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 20. C4×#3633 | C8 | semidirect |
| 23. C4×#3624 | C8 | semidirect |
| 24. C4×#3624 | C8 | semidirect |
| 27. C4×C8×C17 | C8 | semidirect |
| 28. C8×Dic17 | C8 | semidirect |
| 29. C4×#3622 | C8 | semidirect |
| 121. C4×C8 | #3633 | semidirect |
| 122. C17 | #8131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#3633 | 2 |
| (C2×#3633)⋊C8 | 2 |
| C4×C8×#595 | 2 |
| #8131 | 17 |