Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 94 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. #14544547 | C2 | semidirect |
| 2. #14544251 | C2 | semidirect |
| 3. #14544176 | C2 | semidirect |
| 4. #14544157 | C2 | semidirect |
| 5. #14544116 | C2 | semidirect |
| 6. #14544108 | C2 | semidirect |
| 22. Q8×Dic34 | C4 | semidirect |
| 26. #11763524 | C4 | semidirect |
| 28. #11763474 | C4 | semidirect |
| 38. C17×#556 | C4 | semidirect |
| 279. #556 | #595 | semidirect |
| 390. C17 | #8413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544547 | 2 |
| #14544251 | 2 |
| #14544176 | 2 |
| #14544157 | 2 |
| #14544116 | 2 |
| #14544108 | 2 |
| #14542798 | 2 |
| #8413 | 17 |