Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #14531960 | C2 | direct (N × H) |
| 3. C2×#11762687 | C2 | semidirect |
| 4. C2×#11762677 | C2 | semidirect |
| 5. C2×C17×#383 | C2 | semidirect |
| 8. C2×#10587560 | C4 | semidirect |
| 11. #11762687 | C22 | semidirect |
| 12. #11762677 | C22 | semidirect |
| 15. C17×#383 | C22 | semidirect |
| 23. C22×D68 | C2×C4 | semidirect |
| 27. C2×C42×C17 | C2×C4 | semidirect |
| 31. #10587560 | C2×C4 | semidirect |
| 49. C2×D68 | C22×C4 | semidirect |
| 52. C42×C17 | C22×C4 | semidirect |
| 77. C2×#383 | D17 | semidirect |
| 97. #383 | C2×D17 | semidirect |
| 100. C2×C17 | #2380 | semidirect |
| 117. C2×C42 | C4×D17 | semidirect |
| 121. C17 | C2×#2380 | semidirect |
| 141. C42 | C2×C4×D17 | semidirect |
| 172. C2 | #14531960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587560 | 2 |
| #14531960 | 2 |
| C2×#11762687 | 2 |
| C2×#11762677 | 2 |
| C2×C17×#383 | 2 |
| C2×#2380 | 17 |