Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. #20261070 | C2 | semidirect |
| 4. #20261042 | C2 | semidirect |
| 5. #20260957 | C2 | semidirect |
| 6. #20260891 | C2 | semidirect |
| 8. #20260840 | C2 | semidirect |
| 9. #20260833 | C2 | semidirect |
| 10. #20260792 | C2 | semidirect |
| 11. C2×C4×Q8×C97 | C2 | semidirect |
| 132. C97 | #3117 | semidirect |
| 134. C2×C4×Q8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261269 | 2 |
| #20261070 | 2 |
| #20261053 | 2 |
| #20261042 | 2 |
| #20260957 | 2 |
| #20260891 | 2 |
| #20260874 | 2 |
| #20260840 | 2 |
| #20260833 | 2 |
| #20260792 | 2 |
| C2×C4×Q8×C97 | 2 |
| #3117 | 97 |