Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×#11763699 | C2 | semidirect |
| 4. #14543824 | C2 | semidirect |
| 10. #11763704 | C4 | semidirect |
| 11. C22⋊#63216 | C4 | semidirect |
| 16. C2×#10587469 | C4 | semidirect |
| 17. C2×#10587469 | C4 | semidirect |
| 20. C22×#63214 | C4 | semidirect |
| 21. C22×C16×C17 | C4 | semidirect |
| 83. C16×C17 | C22⋊C4 | semidirect |
| 85. #63214 | C22⋊C4 | semidirect |
| 122. C22×C17 | #347 | semidirect |
| 145. C22×C16 | #595 | semidirect |
| 189. C17 | #12616 | semidirect |
| 223. C16 | C22⋊#595 | semidirect |
| 261. C22 | #11763699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545012 | 2 |
| C2×#11763699 | 2 |
| #14544520 | 2 |
| #14543824 | 2 |
| C22×#10587469 | 2 |
| #12616 | 17 |