Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1134 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 333 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. #14545927 | C2 | direct (N × H) |
| 21. C2×C42×C17 | C8 | semidirect |
| 22. C2×C4×Dic17 | C8 | semidirect |
| 23. C42×D17 | C8 | semidirect |
| 44. C42×C17 | C2×C8 | semidirect |
| 45. C4×Dic17 | C2×C8 | semidirect |
| 89. C2×C17 | #1839 | semidirect |
| 91. D17 | #1839 | semidirect |
| 107. C2×C42 | #3633 | semidirect |
| 108. C17 | C2×#1839 | semidirect |
| 129. C42 | C2×#3633 | semidirect |
| 165. C2 | #14545927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545927 | 2 |
| C2×(C2×#3633)⋊C4 | 2 |
| C2×C42×#595 | 2 |
| C2×#1839 | 17 |