Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690832 | C2 | semidirect |
| 2. #20261313 | C2 | semidirect |
| 3. #20260981 | C2 | semidirect |
| 4. #20260976 | C2 | semidirect |
| 5. #20260971 | C2 | semidirect |
| 6. C2×#15690744 | C2 | semidirect |
| 7. #20260737 | C2 | semidirect |
| 8. C2×#131×C97 | C2 | semidirect |
| 56. C2×C8×C97 | D4 | semidirect |
| 109. C97 | #3061 | semidirect |
| 111. C2×#131 | D97 | semidirect |
| 160. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261313 | 2 |
| #20260981 | 2 |
| #20260976 | 2 |
| #20260971 | 2 |
| C2×#15690744 | 2 |
| #20260737 | 2 |
| C2×#131×C97 | 2 |
| #3061 | 97 |