Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
426 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 23. #11762614 | C4 | semidirect |
| 24. #11762613 | C4 | semidirect |
| 25. #11762612 | C4 | semidirect |
| 26. C17×#358 | C4 | semidirect |
| 91. Q16×C17 | C4⋊C4 | semidirect |
| 100. Dic68 | C4⋊C4 | semidirect |
| 190. #358 | #595 | semidirect |
| 236. C17 | #12936 | 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×#11763735 | 2 |
| C2×#11763722 | 2 |
| #14544888 | 2 |
| #14543841 | 2 |
| #14543821 | 2 |
| D17×#358 | 2 |
| #12936 | 17 |