Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
474 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14545626 | C2 | semidirect |
| 2. #14544548 | C2 | semidirect |
| 3. #14544239 | C2 | semidirect |
| 4. #14544173 | C2 | semidirect |
| 5. #14543671 | C2 | semidirect |
| 6. #14543650 | C2 | semidirect |
| 25. #11763094 | C4 | semidirect |
| 26. #11763090 | C4 | semidirect |
| 27. #11763001 | C4 | semidirect |
| 32. C17×#460 | C4 | semidirect |
| 209. #460 | #595 | semidirect |
| 284. C17 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545626 | 2 |
| #14544548 | 2 |
| #14544239 | 2 |
| #14544173 | 2 |
| #14543671 | 2 |
| #14543650 | 2 |
| #14538934 | 2 |
| #9161 | 17 |