Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
486 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 3. #14544257 | C2 | semidirect |
| 4. #14544167 | C2 | semidirect |
| 5. #14543677 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763090 | C4 | semidirect |
| 26. #11763089 | C4 | semidirect |
| 27. #11763011 | C4 | semidirect |
| 32. C17×#461 | C4 | semidirect |
| 217. #461 | #595 | semidirect |
| 292. C17 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545644 | 2 |
| #14544554 | 2 |
| #14544257 | 2 |
| #14544167 | 2 |
| #14543677 | 2 |
| #14543636 | 2 |
| #14538882 | 2 |
| #9165 | 17 |