Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 9. #11763722 | C4 | direct (N × H) |
| 15. C4×Dic68 | C4 | semidirect |
| 16. Q16×Dic17 | C4 | semidirect |
| 17. #11762903 | C4 | semidirect |
| 23. C4×Q16×C17 | C4 | semidirect |
| 76. Q16×C17 | C42 | semidirect |
| 98. Dic68 | C42 | semidirect |
| 149. C4×C17 | #358 | semidirect |
| 155. Dic17 | #358 | semidirect |
| 165. C4×Q16 | #595 | semidirect |
| 217. C17 | C4×#358 | semidirect |
| 233. Q16 | C4×#595 | semidirect |
| 305. C4 | #11763722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763722 | 2 |
| C4×#10587529 | 2 |
| C4×#10587534 | 2 |
| #14543841 | 2 |
| C4×Q16×D17 | 2 |
| C4×#358 | 17 |