Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
452 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14545740 | C2 | semidirect |
| 2. #14544922 | C2 | semidirect |
| 3. #14544156 | C2 | semidirect |
| 4. #14544144 | C2 | semidirect |
| 5. #14543673 | C2 | semidirect |
| 6. #14543669 | C2 | semidirect |
| 26. #11763218 | C4 | semidirect |
| 27. #11763173 | C4 | semidirect |
| 28. #11763168 | C4 | semidirect |
| 34. C17×#496 | C4 | semidirect |
| 220. #496 | #595 | semidirect |
| 305. C17 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545740 | 2 |
| #14544922 | 2 |
| #14544156 | 2 |
| #14544144 | 2 |
| #14543673 | 2 |
| #14543669 | 2 |
| #14539376 | 2 |
| #8997 | 17 |