Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20261290 | C2 | semidirect |
| 3. #20261040 | C2 | semidirect |
| 4. #20261034 | C2 | semidirect |
| 5. #20261030 | C2 | semidirect |
| 6. #20261026 | C2 | semidirect |
| 7. #20261012 | C2 | semidirect |
| 8. #20260770 | C2 | semidirect |
| 9. C4⋊C8×D97 | C2 | semidirect |
| 11. #475×C97 | C2 | semidirect |
| 44. #13095512 | Q8 | semidirect |
| 135. C97 | #3076 | semidirect |
| 142. #475 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4×#13095512 | 2 |
| #20261040 | 2 |
| #20261034 | 2 |
| #20261030 | 2 |
| #20261026 | 2 |
| #20261012 | 2 |
| #20260770 | 2 |
| C4⋊C8×D97 | 2 |
| #20260730 | 2 |
| #475×C97 | 2 |
| #3076 | 97 |