Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545530 | C2 | semidirect |
| 2. #14544947 | C2 | semidirect |
| 3. #14544165 | C2 | semidirect |
| 4. #14544091 | C2 | semidirect |
| 5. #14543619 | C2 | semidirect |
| 6. #14543616 | C2 | semidirect |
| 24. #11763186 | C4 | semidirect |
| 25. #11763157 | C4 | semidirect |
| 26. #11763157 | C4 | semidirect |
| 30. C17×#500 | C4 | semidirect |
| 115. #63243 | D8 | semidirect |
| 219. #500 | #595 | semidirect |
| 293. C17 | #9053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545530 | 2 |
| #14544947 | 2 |
| #14544165 | 2 |
| #14544091 | 2 |
| #14543619 | 2 |
| #14543616 | 2 |
| #14539364 | 2 |
| #9053 | 17 |