Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
442 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 442 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. #14545671 | C2 | semidirect |
| 2. #14544273 | C2 | semidirect |
| 3. #14544205 | C2 | semidirect |
| 4. #14544204 | C2 | semidirect |
| 5. #14543651 | C2 | semidirect |
| 6. #14543644 | C2 | semidirect |
| 20. #11763205 | C4 | semidirect |
| 21. #11763185 | C4 | semidirect |
| 22. #11763156 | C4 | semidirect |
| 26. C17×#486 | C4 | semidirect |
| 174. #486 | #595 | semidirect |
| 234. C17 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545671 | 2 |
| #14544273 | 2 |
| #14544205 | 2 |
| #14544204 | 2 |
| #14543651 | 2 |
| #14543644 | 2 |
| #14539521 | 2 |
| #9417 | 17 |