Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
582 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 132 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. #14544521 | C2 | semidirect |
| 4. #14543627 | C2 | semidirect |
| 6. C23×#3624 | C4 | semidirect |
| 10. C2×C4⋊#3624 | C4 | semidirect |
| 11. C2×C22⋊#3624 | C4 | semidirect |
| 15. C2×C4×#3624 | C4 | semidirect |
| 17. #11763654 | C4 | semidirect |
| 18. #11763652 | C4 | semidirect |
| 113. C23×C17 | #97 | semidirect |
| 126. C2×C4×C17 | #97 | semidirect |
| 151. #3624 | #99 | semidirect |
| 243. C17 | #8160 | semidirect |
| 298. C23 | #10587542 | semidirect |
| 330. C2×C4 | #10587542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3624 | 2 |
| #14544521 | 2 |
| #14544020 | 2 |
| #14543627 | 2 |
| #99×Dic17 | 2 |
| #8160 | 17 |