Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 267 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. C22×#10587471 | C2 | semidirect |
| 2. C2×#11763189 | C2 | semidirect |
| 4. #14531040 | C2 | direct (N × H) |
| 5. C2×C4×C16×C17 | C2 | semidirect |
| 13. C2×#10587471 | C22 | semidirect |
| 15. #11763189 | C22 | semidirect |
| 20. C4×C16×C17 | C22 | semidirect |
| 42. C2×C16×C17 | D4 | semidirect |
| 75. C16×C17 | C2×D4 | semidirect |
| 81. C2×C4×C17 | SD32 | semidirect |
| 103. C2×C4×C16 | D17 | semidirect |
| 111. C4×C17 | C2×SD32 | semidirect |
| 129. C4×C16 | C2×D17 | semidirect |
| 130. C2×C17 | #2248 | semidirect |
| 156. C2×C16 | D68 | semidirect |
| 160. C17 | C2×#2248 | semidirect |
| 189. C16 | C2×D68 | semidirect |
| 203. C2×C4 | #10587471 | semidirect |
| 220. C4 | C2×#10587471 | semidirect |
| 224. C2 | #14531040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587471 | 2 |
| C2×#11763189 | 2 |
| C2×#11763186 | 2 |
| #14531040 | 2 |
| C2×C4×C16×C17 | 2 |
| C2×#2248 | 17 |