Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2190 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 360 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×#10587543 | C2 | semidirect |
| 2. C22×(C2×#595)⋊C4 | C2 | semidirect |
| 3. C2×#11763660 | C2 | direct (N × H) |
| 8. C2×#10587543 | C22 | semidirect |
| 10. C2×(C2×#595)⋊C4 | C22 | semidirect |
| 11. #11763660 | C22 | direct (N × H) |
| 16. C2×#10587624 | C4 | semidirect |
| 18. C22×C4⋊Dic17 | C4 | semidirect |
| 20. C23×D4×C17 | C4 | semidirect |
| 29. C22×D4×C17 | C2×C4 | semidirect |
| 49. #10587624 | C2×C4 | semidirect |
| 52. C2×C4⋊Dic17 | C2×C4 | semidirect |
| 54. (C2×#595)⋊C4 | C23 | semidirect |
| 56. #10587543 | C23 | semidirect |
| 76. C2×D4×C17 | C22×C4 | semidirect |
| 104. C4⋊Dic17 | C22×C4 | semidirect |
| 159. C22×C17 | #327 | semidirect |
| 181. C23×D4 | #595 | semidirect |
| 197. C2×C17 | C2×#327 | semidirect |
| 212. C22×D4 | C2×#595 | semidirect |
| 240. C17 | C22×#327 | semidirect |
| 260. C2×D4 | C22×#595 | semidirect |
| 348. C22 | #11763660 | direct (N × H) |
| 363. C2 | C2×#11763660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587543 | 2 |
| C22×(C2×#595)⋊C4 | 2 |
| C2×#11763660 | 2 |
| C22×#10587624 | 2 |
| C22×#327 | 17 |