Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
474 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 1. C8×C4⋊#595 | C2 | semidirect |
| 4. #14543998 | C2 | semidirect |
| 5. #14543680 | C2 | semidirect |
| 6. #14543674 | C2 | semidirect |
| 14. #11763668 | C4 | semidirect |
| 15. #11763667 | C4 | semidirect |
| 22. #11762888 | C4 | semidirect |
| 24. D4×#3622 | C4 | semidirect |
| 25. #11762874 | C4 | semidirect |
| 30. C17×#436 | C4 | semidirect |
| 205. #436 | #595 | semidirect |
| 275. C17 | #8257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#595 | 2 |
| #14544281 | 2 |
| #14544163 | 2 |
| #14543998 | 2 |
| #14543680 | 2 |
| #14543674 | 2 |
| #14537493 | 2 |
| #8257 | 17 |