Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
934 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×#11763722 | C2 | semidirect |
| 13. C22×Dic68 | C4 | semidirect |
| 18. C2×Q16×D17 | C4 | semidirect |
| 21. C22×Q16×C17 | C4 | semidirect |
| 98. Q16×C17 | C22⋊C4 | semidirect |
| 109. Dic68 | C22⋊C4 | semidirect |
| 163. C22×C17 | #358 | semidirect |
| 169. C2×D17 | #358 | semidirect |
| 190. C22×Q16 | #595 | semidirect |
| 245. C17 | #12732 | semidirect |
| 285. Q16 | C22⋊#595 | semidirect |
| 352. C22 | #11763722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763722 | 2 |
| #14545009 | 2 |
| #14544661 | 2 |
| C22×Q16×D17 | 2 |
| #12732 | 17 |