Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 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. #20260496 | C2 | semidirect |
| 8. #15690797 | C4 | semidirect |
| 21. C2×Dic194 | C2×C4 | semidirect |
| 31. C4×Dic97 | C2×C4 | semidirect |
| 81. C97 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690797 | 2 |
| #20261210 | 2 |
| #20260745 | 2 |
| #20260496 | 2 |
| C2×#100×C97 | 2 |
| #1885 | 97 |