Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20260745 | C2 | semidirect |
| 4. C2×#15690728 | C2 | semidirect |
| 5. #20260507 | C2 | semidirect |
| 6. #20260493 | C2 | semidirect |
| 11. C2×#13095501 | C4 | semidirect |
| 12. C2×#13095499 | C4 | semidirect |
| 108. C97 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| #20260752 | 2 |
| #20260745 | 2 |
| C2×#15690728 | 2 |
| #20260507 | 2 |
| #20260493 | 2 |
| #568×C97 | 2 |
| #1902 | 97 |