Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20260630 | C2 | semidirect |
| 3. #20260629 | C2 | semidirect |
| 4. #20260623 | C2 | semidirect |
| 5. #20260619 | C2 | semidirect |
| 7. #20260607 | C2 | semidirect |
| 8. #20260593 | C2 | semidirect |
| 12. #15690791 | C4 | semidirect |
| 36. C22×Dic97 | C2×C4 | semidirect |
| 44. #13095490 | C2×C4 | semidirect |
| 48. C22⋊Dic97 | C2×C4 | semidirect |
| 127. C97 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690791 | 2 |
| #20260630 | 2 |
| #20260629 | 2 |
| #20260623 | 2 |
| #20260619 | 2 |
| #20260615 | 2 |
| #20260607 | 2 |
| #20260593 | 2 |
| #390×C97 | 2 |
| #2376 | 97 |