Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
436 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14545610 | C2 | semidirect |
| 2. #14544254 | C2 | semidirect |
| 3. #14544213 | C2 | semidirect |
| 4. #14544196 | C2 | semidirect |
| 5. #14543678 | C2 | semidirect |
| 6. #14543661 | C2 | semidirect |
| 26. #11763218 | C4 | semidirect |
| 27. #11763173 | C4 | semidirect |
| 28. #11763168 | C4 | semidirect |
| 34. C17×#496 | C4 | semidirect |
| 212. #496 | #595 | semidirect |
| 296. C17 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545610 | 2 |
| #14544254 | 2 |
| #14544213 | 2 |
| #14544196 | 2 |
| #14543678 | 2 |
| #14543661 | 2 |
| #14539479 | 2 |
| #9432 | 17 |