Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20261218 | C2 | semidirect |
| 3. #20260745 | C2 | semidirect |
| 4. #20260737 | C2 | semidirect |
| 5. #20260732 | C2 | semidirect |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#131×C97 | C2 | semidirect |
| 9. #15690857 | C4 | semidirect |
| 28. #13095511 | C2×C4 | semidirect |
| 32. C2×Dic194 | C2×C4 | semidirect |
| 95. C97 | #2898 | semidirect |
| 97. C2×#131 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| #20261218 | 2 |
| #20260745 | 2 |
| #20260737 | 2 |
| #20260732 | 2 |
| C2×#15690735 | 2 |
| C2×#131×C97 | 2 |
| #2898 | 97 |