Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20261458 | C2 | semidirect |
| 3. #20261085 | C2 | semidirect |
| 4. #20261075 | C2 | semidirect |
| 5. #20261016 | C2 | semidirect |
| 6. #20260973 | C2 | semidirect |
| 7. #20260896 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. #20260800 | C2 | semidirect |
| 10. #20260730 | C2 | semidirect |
| 11. #462×C97 | C2 | semidirect |
| 126. C97 | #3302 | semidirect |
| 133. #462 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261388 | 2 |
| #20261085 | 2 |
| #20261075 | 2 |
| #20261016 | 2 |
| #20260973 | 2 |
| #20260896 | 2 |
| C4×#13095498 | 2 |
| #20260800 | 2 |
| #20260730 | 2 |
| #462×C97 | 2 |
| #3302 | 97 |