Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
190 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #14543950 | C2 | direct (N × H) |
| 12. #11762642 | C4 | semidirect |
| 14. C2×#10587465 | C4 | semidirect |
| 15. C2×C17×C32 | C4 | semidirect |
| 29. C17×C32 | C2×C4 | semidirect |
| 30. #10587465 | C2×C4 | semidirect |
| 82. C2×C32 | #595 | semidirect |
| 87. C2×C17 | #1426 | semidirect |
| 105. C32 | C2×#595 | semidirect |
| 106. C17 | C2×#1426 | semidirect |
| 149. C2 | #14543950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763738 | 2 |
| C2×#11763736 | 2 |
| #14543950 | 2 |
| C2×#11762642 | 2 |
| C2×#1426 | 17 |