Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. #20260633 | C2 | semidirect |
| 4. #20260599 | C2 | semidirect |
| 6. C4×C4⋊Dic97 | C2 | semidirect |
| 7. #20260580 | C2 | semidirect |
| 9. #15690769 | C4 | semidirect |
| 95. C97 | #2346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690769 | 2 |
| #20260633 | 2 |
| #20260623 | 2 |
| #20260599 | 2 |
| #20260595 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260580 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2346 | 97 |