Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
430 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. C2×#11763696 | C2 | semidirect |
| 4. #14544588 | C2 | semidirect |
| 5. #14543845 | C2 | semidirect |
| 6. #14543844 | C2 | semidirect |
| 11. #11763853 | C4 | semidirect |
| 17. #11763724 | C4 | semidirect |
| 23. #11762613 | C4 | semidirect |
| 24. #11762611 | C4 | semidirect |
| 25. #11762609 | C4 | semidirect |
| 26. C17×#358 | C4 | semidirect |
| 175. #358 | #595 | semidirect |
| 223. C17 | #12642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763853 | 2 |
| C2×#11763724 | 2 |
| C2×#11763696 | 2 |
| #14544588 | 2 |
| #14543845 | 2 |
| #14543844 | 2 |
| #14530490 | 2 |
| #12642 | 17 |