Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
392 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14544504 | C2 | semidirect |
| 4. #14543992 | C2 | semidirect |
| 5. #14543678 | C2 | semidirect |
| 6. #14543673 | C2 | semidirect |
| 8. #11763860 | C4 | semidirect |
| 9. Q8×#3624 | C4 | semidirect |
| 10. #11763844 | C4 | semidirect |
| 13. D4×#3624 | C4 | semidirect |
| 29. #11762550 | C4 | semidirect |
| 30. #11762550 | C4 | semidirect |
| 31. #11762549 | C4 | semidirect |
| 32. C17×#329 | C4 | semidirect |
| 200. #329 | #595 | semidirect |
| 253. C17 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545598 | 2 |
| #14544504 | 2 |
| #14544156 | 2 |
| #14543992 | 2 |
| #14543678 | 2 |
| #14543673 | 2 |
| #14527369 | 2 |
| #8248 | 17 |