Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
522 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14544520 | C2 | semidirect |
| 2. C8×C22⋊#595 | C2 | semidirect |
| 5. #14543666 | C2 | semidirect |
| 6. #14543664 | C2 | semidirect |
| 16. #11763662 | C4 | semidirect |
| 17. #11763662 | C4 | semidirect |
| 18. #11763661 | C4 | semidirect |
| 19. #11763661 | C4 | semidirect |
| 20. C2×#10587587 | C4 | semidirect |
| 27. #11762836 | C4 | semidirect |
| 28. #11762777 | C4 | semidirect |
| 30. C17×#405 | C4 | semidirect |
| 221. #405 | #595 | semidirect |
| 284. C17 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544520 | 2 |
| C8×C22⋊#595 | 2 |
| #14544161 | 2 |
| #14543666 | 2 |
| #14543664 | 2 |
| #14537480 | 2 |
| #8240 | 17 |