Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 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. #20261081 | C2 | semidirect |
| 4. #20261058 | C2 | semidirect |
| 5. #20261021 | C2 | semidirect |
| 6. #20260961 | C2 | semidirect |
| 7. #20260894 | C2 | semidirect |
| 8. C4×#13095501 | C2 | semidirect |
| 9. #20260800 | C2 | semidirect |
| 10. #20260728 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 128. C97 | #3304 | semidirect |
| 135. #460 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261405 | 2 |
| #20261081 | 2 |
| #20261058 | 2 |
| #20261021 | 2 |
| #20260961 | 2 |
| #20260894 | 2 |
| C4×#13095501 | 2 |
| #20260800 | 2 |
| #20260728 | 2 |
| #460×C97 | 2 |
| #3304 | 97 |