Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14545564 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. #14545100 | C2 | semidirect |
| 4. #14544943 | C2 | semidirect |
| 5. #14543846 | C2 | semidirect |
| 6. #14543837 | C2 | semidirect |
| 24. C2×#10587499 | C4 | semidirect |
| 25. C2×#10587499 | C4 | semidirect |
| 26. C2×D272 | C4 | semidirect |
| 28. C2×C17×Q32 | C4 | semidirect |
| 189. C2×Q32 | #595 | semidirect |
| 255. C17 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545564 | 2 |
| #14545106 | 2 |
| #14545100 | 2 |
| #14544943 | 2 |
| #14543846 | 2 |
| #14543837 | 2 |
| C2×#11763242 | 2 |
| #13016 | 17 |