Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
700 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 102 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. #14544963 | C2 | semidirect |
| 3. #14544301 | C2 | semidirect |
| 4. #14544294 | C2 | semidirect |
| 5. #14544166 | C2 | semidirect |
| 22. #11763537 | C4 | semidirect |
| 24. #11763533 | C4 | semidirect |
| 25. #11763532 | C4 | semidirect |
| 38. C17×#557 | C4 | semidirect |
| 291. #557 | #595 | semidirect |
| 404. C17 | #8427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544963 | 2 |
| #14544659 | 2 |
| #14544301 | 2 |
| #14544294 | 2 |
| #14544166 | 2 |
| #14544082 | 2 |
| #14542667 | 2 |
| #8427 | 17 |