Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20261470 | C2 | semidirect |
| 2. #20261442 | C2 | semidirect |
| 3. #20261091 | C2 | semidirect |
| 4. #20261082 | C2 | semidirect |
| 5. #20261034 | C2 | semidirect |
| 6. #20261030 | C2 | semidirect |
| 7. #20260952 | C2 | semidirect |
| 9. C8×Dic194 | C2 | semidirect |
| 10. #20260815 | C2 | semidirect |
| 11. C4×SD16×C97 | C2 | semidirect |
| 123. C97 | #3361 | semidirect |
| 133. C4×SD16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261470 | 2 |
| #20261442 | 2 |
| #20261091 | 2 |
| #20261082 | 2 |
| #20261034 | 2 |
| #20261030 | 2 |
| #20260952 | 2 |
| #20260930 | 2 |
| C8×Dic194 | 2 |
| #20260815 | 2 |
| C4×SD16×C97 | 2 |
| #3361 | 97 |