Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #20260778 | C2 | semidirect |
| 4. #20260776 | C2 | semidirect |
| 5. #20260770 | C2 | semidirect |
| 6. C2×#15690742 | C2 | semidirect |
| 7. #106×D97 | C2 | semidirect |
| 8. #427×C97 | C2 | semidirect |
| 10. #15690816 | C4 | semidirect |
| 37. #13095495 | C2×C4 | semidirect |
| 38. #13095494 | C2×C4 | semidirect |
| 40. C8×D97 | C2×C4 | semidirect |
| 47. C2×C8×C97 | C2×C4 | semidirect |
| 91. C97 | #2912 | semidirect |
| 97. #427 | D97 | semidirect |
| 133. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261215 | 2 |
| #20260778 | 2 |
| #20260776 | 2 |
| #20260770 | 2 |
| C2×#15690742 | 2 |
| #106×D97 | 2 |
| #427×C97 | 2 |
| #2912 | 97 |