Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20260796 | C2 | semidirect |
| 2. #20260759 | C2 | semidirect |
| 4. C4×#13095495 | C2 | semidirect |
| 7. C4⋊#11715895 | C22 | semidirect |
| 9. #15690721 | C22 | semidirect |
| 10. C4×#11715895 | C22 | semidirect |
| 66. C97 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260796 | 2 |
| #20260759 | 2 |
| #20260699 | 2 |
| C4×#13095495 | 2 |
| C2×#117×C97 | 2 |
| #2921 | 97 |