Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
382 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. #14545007 | C2 | semidirect |
| 4. #14543839 | C2 | semidirect |
| 7. C2×#10587538 | C4 | semidirect |
| 10. C22×#63216 | C4 | semidirect |
| 12. #11763705 | C4 | semidirect |
| 144. C17 | #12617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763867 | 2 |
| #14545020 | 2 |
| #14545007 | 2 |
| #14543839 | 2 |
| #14528587 | 2 |
| #12617 | 17 |