Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
496 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 496 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. #14544950 | C2 | semidirect |
| 4. #14544300 | C2 | semidirect |
| 5. #14543680 | C2 | semidirect |
| 6. #14543653 | C2 | semidirect |
| 24. #11763104 | C4 | semidirect |
| 25. #11763100 | C4 | semidirect |
| 26. #11763096 | C4 | semidirect |
| 32. C17×#477 | C4 | semidirect |
| 147. Q8×C17 | #103 | semidirect |
| 162. D68 | #103 | semidirect |
| 218. #477 | #595 | semidirect |
| 296. C17 | #9317 | semidirect |
| 360. Q8 | #10587549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545702 | 2 |
| #14544950 | 2 |
| #14544659 | 2 |
| #14544300 | 2 |
| #14543680 | 2 |
| #14543653 | 2 |
| #14538598 | 2 |
| #9317 | 17 |