Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261550 | C2 | semidirect |
| 2. #20261549 | C2 | semidirect |
| 3. #20261113 | C2 | semidirect |
| 4. #20261010 | C2 | semidirect |
| 5. #20261008 | C2 | semidirect |
| 6. #20261007 | C2 | semidirect |
| 7. #20260918 | C2 | semidirect |
| 8. #20260916 | C2 | semidirect |
| 9. #20260852 | C2 | semidirect |
| 10. #20260850 | C2 | semidirect |
| 11. #578×C97 | C2 | semidirect |
| 147. C97 | #3293 | semidirect |
| 150. #578 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261550 | 2 |
| #20261549 | 2 |
| #20261113 | 2 |
| #20261010 | 2 |
| #20261008 | 2 |
| #20261007 | 2 |
| #20260918 | 2 |
| #20260916 | 2 |
| #20260852 | 2 |
| #20260850 | 2 |
| #578×C97 | 2 |
| #3293 | 97 |