Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
238 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 126 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. #14543890 | C2 | semidirect |
| 4. C32×#595 | C2 | semidirect |
| 8. #11763740 | C4 | semidirect |
| 11. C2×#10587467 | C4 | semidirect |
| 15. #11762643 | C4 | semidirect |
| 16. #11762642 | C4 | semidirect |
| 18. C17×M64 | C4 | semidirect |
| 88. M64 | #595 | semidirect |
| 118. C17 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763740 | 2 |
| #14544992 | 2 |
| #14543890 | 2 |
| C32×#595 | 2 |
| D17×M64 | 2 |
| #13549 | 17 |