Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1006 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 25. C4×C8×C17 | Q8 | semidirect |
| 52. C8×C17 | C4⋊Q8 | semidirect |
| 61. C4×C17 | #498 | semidirect |
| 87. C4×C8 | Dic34 | semidirect |
| 89. C17 | #33310 | semidirect |
| 114. C8 | #10587555 | semidirect |
| 120. C4 | #11763207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763207 | 2 |
| #14537182 | 2 |
| #14528941 | 2 |
| C42×C8×C17 | 2 |
| #33310 | 17 |