Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
330 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 172 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. #14543695 | C2 | semidirect |
| 4. C16×#3624 | C2 | semidirect |
| 26. #10587530 | C8 | semidirect |
| 35. C16×D17 | C8 | semidirect |
| 36. C16×D17 | C8 | semidirect |
| 117. C17 | #11399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544991 | 2 |
| #14543988 | 2 |
| #14543695 | 2 |
| C16×#3624 | 2 |
| C4×C16×D17 | 2 |
| #11399 | 17 |