Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
7902 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7902 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×C22⋊#595 | C2 | semidirect |
| 2. C22×#10587539 | C2 | direct (N × H) |
| 6. C22×C22⋊#595 | C22 | semidirect |
| 7. C2×#10587539 | C22 | direct (N × H) |
| 8. C25×D17 | C4 | semidirect |
| 12. C23×D68 | C4 | semidirect |
| 14. C24×C4×C17 | C4 | semidirect |
| 21. C24×D17 | C2×C4 | semidirect |
| 29. C23×C4×C17 | C2×C4 | semidirect |
| 34. C22×D68 | C2×C4 | semidirect |
| 37. C2×C22⋊#595 | C23 | semidirect |
| 38. #10587539 | C23 | direct (N × H) |
| 55. C23×D17 | C22×C4 | semidirect |
| 63. C22×C4×C17 | C22×C4 | semidirect |
| 68. C2×D68 | C22×C4 | semidirect |
| 71. C22⋊#595 | C24 | semidirect |
| 75. C23×C17 | #99 | semidirect |
| 93. C22×D17 | C23×C4 | semidirect |
| 101. C2×C4×C17 | C23×C4 | semidirect |
| 109. C22×C17 | C2×#99 | semidirect |
| 134. C24×C4 | #595 | semidirect |
| 140. C2×C17 | C22×#99 | semidirect |
| 165. C23×C4 | C2×#595 | semidirect |
| 169. C17 | C23×#99 | semidirect |
| 200. C22×C4 | C22×#595 | semidirect |
| 223. C23 | #10587539 | direct (N × H) |
| 233. C2×C4 | C23×#595 | semidirect |
| 248. C22 | C2×#10587539 | direct (N × H) |
| 259. C2 | C22×#10587539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊#595 | 2 |
| C22×#10587539 | 2 |
| C24×D68 | 2 |
| C23×#99 | 17 |