Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 12. #15690721 | C4 | semidirect |
| 13. C4×#11715895 | C4 | semidirect |
| 73. C97 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095495 | 2 |
| #20260507 | 2 |
| #20260505 | 2 |
| #20260495 | 2 |
| #20260493 | 2 |
| #20260491 | 2 |
| #339×C97 | 2 |
| #1841 | 97 |