Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #14529623 | C2 | semidirect |
| 3. #14527575 | C2 | semidirect |
| 4. #14527453 | C2 | semidirect |
| 5. #14527201 | C2 | semidirect |
| 6. #14526673 | C2 | semidirect |
| 7. C17×#1560 | C2 | semidirect |
| 150. #1560 | D17 | semidirect |
| 236. C17 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14529623 | 2 |
| #14527575 | 2 |
| #14527453 | 2 |
| #14527201 | 2 |
| #14526673 | 2 |
| C17×#1560 | 2 |
| #10488 | 17 |