Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14545749 | C2 | semidirect |
| 2. D17⋊#361 | C2 | semidirect |
| 3. C2×#11763721 | C2 | semidirect |
| 4. #14544673 | C2 | semidirect |
| 5. #14543860 | C2 | semidirect |
| 6. #14543843 | C2 | semidirect |
| 25. #11763080 | C4 | semidirect |
| 26. #11763079 | C4 | semidirect |
| 29. #11763076 | C4 | semidirect |
| 32. C17×#472 | C4 | semidirect |
| 243. #472 | #595 | semidirect |
| 316. C17 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545749 | 2 |
| D17⋊#361 | 2 |
| C2×#11763721 | 2 |
| #14544673 | 2 |
| #14543860 | 2 |
| #14543843 | 2 |
| D17×#472 | 2 |
| #13073 | 17 |