Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20261501 | C2 | semidirect |
| 3. #20260751 | C2 | semidirect |
| 4. #20260732 | C2 | semidirect |
| 5. #20260701 | C2 | semidirect |
| 6. #20260507 | C2 | semidirect |
| 7. #341×C97 | C2 | semidirect |
| 11. #15690843 | C4 | semidirect |
| 13. #15690838 | C4 | semidirect |
| 119. C97 | #1881 | semidirect |
| 126. #341 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261535 | 2 |
| #20261501 | 2 |
| #20260751 | 2 |
| #20260732 | 2 |
| #20260701 | 2 |
| #20260507 | 2 |
| #341×C97 | 2 |
| #1881 | 97 |