Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
262 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. #14543815 | C2 | direct (N × H) |
| 18. C2×C16×C17 | C8 | semidirect |
| 42. C16×C17 | C2×C8 | semidirect |
| 86. C2×C17 | #1371 | semidirect |
| 96. C2×C16 | #3624 | semidirect |
| 104. C17 | C2×#1371 | semidirect |
| 122. C16 | C2×#3624 | semidirect |
| 153. C2 | #14543815 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763672 | 2 |
| #14543815 | 2 |
| C2×C16×Dic17 | 2 |
| C2×#1371 | 17 |