Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20261470 | C2 | semidirect |
| 2. #20261124 | C2 | semidirect |
| 3. #20261119 | C2 | semidirect |
| 4. #20260958 | C2 | semidirect |
| 5. #20260951 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260837 | C2 | semidirect |
| 8. C4×D776 | C2 | semidirect |
| 9. #446×C97 | C2 | semidirect |
| 109. C97 | #3403 | semidirect |
| 116. #446 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261470 | 2 |
| #20261124 | 2 |
| #20261119 | 2 |
| #20260958 | 2 |
| #20260951 | 2 |
| #20260931 | 2 |
| #20260837 | 2 |
| C4×D776 | 2 |
| #446×C97 | 2 |
| #3403 | 97 |