Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261138 | C2 | semidirect |
| 3. #20261073 | C2 | semidirect |
| 4. #20261048 | C2 | semidirect |
| 5. #20261030 | C2 | semidirect |
| 6. #20261022 | C2 | semidirect |
| 7. #20260983 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. #20260813 | C2 | semidirect |
| 10. #20260775 | C2 | semidirect |
| 11. #554×C97 | C2 | semidirect |
| 122. C97 | #3357 | semidirect |
| 124. #554 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261450 | 2 |
| #20261138 | 2 |
| #20261073 | 2 |
| #20261048 | 2 |
| #20261030 | 2 |
| #20261022 | 2 |
| #20260983 | 2 |
| C4×#13095498 | 2 |
| #20260813 | 2 |
| #20260775 | 2 |
| #554×C97 | 2 |
| #3357 | 97 |