Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1134 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 432 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. #14544711 | C2 | direct (N × H) |
| 16. C2×C42×C17 | C8 | semidirect |
| 37. C42×C17 | C2×C8 | semidirect |
| 78. C2×C17 | #1839 | semidirect |
| 92. C2×C42 | #3624 | semidirect |
| 94. C17 | C2×#1839 | semidirect |
| 112. C42 | C2×#3624 | semidirect |
| 139. C2 | #14544711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544711 | 2 |
| C2×#11763675 | 2 |
| C2×C42×Dic17 | 2 |
| C2×#1839 | 17 |