Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #20261455 | C2 | semidirect |
| 2. #20261138 | C2 | semidirect |
| 3. #20261070 | C2 | semidirect |
| 4. #20261056 | C2 | semidirect |
| 5. #20261017 | C2 | semidirect |
| 6. #20261015 | C2 | semidirect |
| 7. #20260979 | C2 | semidirect |
| 8. C4×#13095499 | C2 | semidirect |
| 9. #20260813 | C2 | semidirect |
| 10. #20260775 | C2 | semidirect |
| 99. #11715895 | #41 | semidirect |
| 123. C97 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261455 | 2 |
| #20261138 | 2 |
| #20261070 | 2 |
| #20261056 | 2 |
| #20261017 | 2 |
| #20261015 | 2 |
| #20260979 | 2 |
| C4×#13095499 | 2 |
| #20260813 | 2 |
| #20260775 | 2 |
| #547×C97 | 2 |
| #3353 | 97 |