Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 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. C2×#15690801 | C2 | semidirect |
| 3. #20261044 | C2 | semidirect |
| 4. #20261040 | C2 | semidirect |
| 5. #20261037 | C2 | semidirect |
| 6. #20261033 | C2 | semidirect |
| 7. #20260777 | C2 | semidirect |
| 8. #20260775 | C2 | semidirect |
| 9. #20260758 | C2 | semidirect |
| 136. C97 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690801 | 2 |
| #41×Dic97 | 2 |
| #20261044 | 2 |
| #20261040 | 2 |
| #20261037 | 2 |
| #20261033 | 2 |
| #20260777 | 2 |
| #20260775 | 2 |
| #20260758 | 2 |
| #20260736 | 2 |
| #417×C97 | 2 |
| #3080 | 97 |