Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
406 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 118 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. #14543741 | C2 | semidirect |
| 4. #14543740 | C2 | semidirect |
| 30. Q16×D17 | C8 | semidirect |
| 70. Q16×C17 | C2×C8 | semidirect |
| 92. Dic68 | C2×C8 | semidirect |
| 168. D17 | #1332 | semidirect |
| 203. C17 | C2×#1332 | semidirect |
| 218. Q16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587529 | 2 |
| #14544329 | 2 |
| #14543741 | 2 |
| #14543740 | 2 |
| C4×Q16×D17 | 2 |
| C2×#1332 | 17 |