Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic97 | C2 | semidirect |
| 2. #20261068 | C2 | semidirect |
| 3. #20261063 | C2 | semidirect |
| 4. #20261051 | C2 | semidirect |
| 5. #20261046 | C2 | semidirect |
| 6. #20260778 | C2 | semidirect |
| 7. #20260736 | C2 | semidirect |
| 8. #20260699 | C2 | semidirect |
| 18. #15690743 | C22 | semidirect |
| 19. #15690741 | C22 | semidirect |
| 20. #15690734 | C22 | semidirect |
| 21. #15690731 | C22 | semidirect |
| 131. C97 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic97 | 2 |
| #20261068 | 2 |
| #20261063 | 2 |
| #20261051 | 2 |
| #20261046 | 2 |
| #20260778 | 2 |
| #20260736 | 2 |
| #20260699 | 2 |
| #525×C97 | 2 |
| #3092 | 97 |