Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
424 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 72 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. #14545604 | C2 | semidirect |
| 2. #14544225 | C2 | semidirect |
| 3. #14544205 | C2 | semidirect |
| 4. #14544105 | C2 | semidirect |
| 5. #14543645 | C2 | semidirect |
| 6. #14543640 | C2 | semidirect |
| 26. #11763199 | C4 | semidirect |
| 27. #11763177 | C4 | semidirect |
| 28. #11763174 | C4 | semidirect |
| 34. C17×#497 | C4 | semidirect |
| 208. #497 | #595 | semidirect |
| 292. C17 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545604 | 2 |
| #14544225 | 2 |
| #14544205 | 2 |
| #14544105 | 2 |
| #14543645 | 2 |
| #14543640 | 2 |
| #14539818 | 2 |
| #9370 | 17 |