Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
846 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 184 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. #14545509 | C2 | semidirect |
| 2. #14544917 | C2 | semidirect |
| 3. #14544774 | C2 | semidirect |
| 4. #14544708 | C2 | semidirect |
| 5. #14544497 | C2 | semidirect |
| 21. #11763194 | C4 | semidirect |
| 22. #11763186 | C4 | semidirect |
| 23. #11763183 | C4 | semidirect |
| 25. C17×#494 | C4 | semidirect |
| 148. #494 | #595 | semidirect |
| 201. C17 | #22280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545509 | 2 |
| #14544917 | 2 |
| #14544774 | 2 |
| #14544708 | 2 |
| #14544497 | 2 |
| #14539213 | 2 |
| #22280 | 17 |