Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
692 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 225 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 |
|---|---|---|
| 33. C17×#125 | C8 | semidirect |
| 36. #10587576 | C8 | semidirect |
| 37. #10587575 | C8 | semidirect |
| 39. #10587556 | C8 | semidirect |
| 145. #125 | #3633 | semidirect |
| 162. C17 | #23263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545931 | 2 |
| C4⋊C4×#3633 | 2 |
| #14545918 | 2 |
| #125×#595 | 2 |
| #23263 | 17 |