Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #14537037 | C2 | direct (N × H) |
| 2. C2×#11762721 | C2 | semidirect |
| 5. C23×Dic34 | C22 | semidirect |
| 7. #11762721 | C22 | semidirect |
| 9. C2×#10587502 | C22 | semidirect |
| 14. C25×C17 | Q8 | semidirect |
| 20. C22×Dic34 | C23 | semidirect |
| 25. #10587502 | C23 | semidirect |
| 32. C24×C17 | C2×Q8 | semidirect |
| 85. C2×C17 | #2840 | semidirect |
| 89. C25 | Dic34 | semidirect |
| 101. C17 | C2×#2840 | semidirect |
| 108. C24 | C2×Dic34 | semidirect |
| 148. C2 | #14537037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537037 | 2 |
| C2×#11762721 | 2 |
| C2×#11762665 | 2 |
| C2×C17×#379 | 2 |
| C2×#2840 | 17 |