Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #20261813 | C2 | semidirect |
| 2. #20261722 | C2 | semidirect |
| 3. #20261721 | C2 | semidirect |
| 4. D97⋊#100 | C2 | semidirect |
| 5. C2×#15690870 | C2 | semidirect |
| 8. D97⋊M16 | C22 | semidirect |
| 9. C2×#13095520 | C22 | semidirect |
| 10. #15690871 | C22 | semidirect |
| 11. #15690870 | C22 | semidirect |
| 12. #15690870 | C22 | semidirect |
| 132. C97 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261813 | 2 |
| #20261722 | 2 |
| #20261721 | 2 |
| D97⋊#100 | 2 |
| C2×#15690870 | 2 |
| C2×#15690855 | 2 |
| #2888 | 97 |