Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 11. Q16×#595 | C4 | semidirect |
| 17. #11763722 | C4 | semidirect |
| 23. #11762614 | C4 | semidirect |
| 24. #11762613 | C4 | semidirect |
| 25. #11762612 | C4 | semidirect |
| 26. C17×#358 | C4 | semidirect |
| 91. Q16×C17 | C42 | semidirect |
| 100. Dic68 | C42 | semidirect |
| 189. #358 | #595 | semidirect |
| 236. C17 | #12638 | semidirect |
| 256. Q16 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#595 | 2 |
| C2×#11763722 | 2 |
| C2×#11763696 | 2 |
| #107×#595 | 2 |
| #14543842 | 2 |
| #14543841 | 2 |
| D17×#358 | 2 |
| #12638 | 17 |