Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
302 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14543934 | C2 | direct (N × H) |
| 12. C2×Dic136 | C4 | semidirect |
| 16. Q32×D17 | C4 | semidirect |
| 19. C2×C17×Q32 | C4 | semidirect |
| 33. C17×Q32 | C2×C4 | semidirect |
| 39. Dic136 | C2×C4 | semidirect |
| 120. C2×Q32 | #595 | semidirect |
| 128. C2×C17 | #1416 | semidirect |
| 130. D17 | #1416 | semidirect |
| 148. Q32 | C2×#595 | semidirect |
| 158. C17 | C2×#1416 | semidirect |
| 225. C2 | #14543934 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763740 | 2 |
| C2×#11763735 | 2 |
| #14543934 | 2 |
| C2×Q32×D17 | 2 |
| C2×#1416 | 17 |