Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1030 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 226 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. #14545686 | C2 | semidirect |
| 2. #14545224 | C2 | semidirect |
| 3. #14544186 | C2 | semidirect |
| 4. #14544173 | C2 | semidirect |
| 5. #14544164 | C2 | semidirect |
| 6. #14544155 | C2 | semidirect |
| 21. #11763545 | C4 | semidirect |
| 22. Q8×Dic34 | C4 | semidirect |
| 23. #11763516 | C4 | semidirect |
| 31. C17×#550 | C4 | semidirect |
| 188. #550 | #595 | semidirect |
| 262. C17 | #17550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545686 | 2 |
| #14545224 | 2 |
| #14544186 | 2 |
| #14544173 | 2 |
| #14544164 | 2 |
| #14544155 | 2 |
| #14542864 | 2 |
| #17550 | 17 |