Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14543745 | C2 | semidirect |
| 4. #14543744 | C2 | semidirect |
| 30. Q16×D17 | C8 | semidirect |
| 70. Q16×C17 | C2×C8 | semidirect |
| 92. Dic68 | C2×C8 | semidirect |
| 166. D17 | #1334 | semidirect |
| 201. C17 | C2×#1334 | semidirect |
| 216. Q16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544985 | 2 |
| #14544326 | 2 |
| #14543745 | 2 |
| #14543744 | 2 |
| C4×Q16×D17 | 2 |
| C2×#1334 | 17 |