Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
548 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545305 | C2 | semidirect |
| 2. #14544215 | C2 | semidirect |
| 3. #14544165 | C2 | semidirect |
| 4. #14544084 | C2 | semidirect |
| 5. #14543680 | C2 | semidirect |
| 6. #14543639 | C2 | semidirect |
| 27. #11763011 | C4 | semidirect |
| 28. #11763005 | C4 | semidirect |
| 29. #11763004 | C4 | semidirect |
| 32. C17×#461 | C4 | semidirect |
| 247. #461 | #595 | semidirect |
| 324. C17 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545305 | 2 |
| #14544215 | 2 |
| #14544165 | 2 |
| #14544084 | 2 |
| #14543680 | 2 |
| #14543639 | 2 |
| #14538249 | 2 |
| #9181 | 17 |