Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
696 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14544655 | C2 | semidirect |
| 3. #14544216 | C2 | semidirect |
| 5. #14544094 | C2 | semidirect |
| 6. #14544087 | C2 | semidirect |
| 24. #11763533 | C4 | semidirect |
| 26. #11763519 | C4 | semidirect |
| 27. #11763516 | C4 | semidirect |
| 38. C17×#556 | C4 | semidirect |
| 295. #556 | #595 | semidirect |
| 407. C17 | #8431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544655 | 2 |
| #14544281 | 2 |
| #14544216 | 2 |
| #14544214 | 2 |
| #14544094 | 2 |
| #14544087 | 2 |
| #14542639 | 2 |
| #8431 | 17 |