Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#15690816 | C2 | semidirect |
| 3. C2×#15690738 | C2 | semidirect |
| 4. C2×#15690738 | C2 | semidirect |
| 5. #20260701 | C2 | semidirect |
| 6. #20260500 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 12. C2×Dic388 | C4 | semidirect |
| 13. C2×#13095500 | C4 | semidirect |
| 14. C2×#13095500 | C4 | semidirect |
| 15. C2×D776 | C4 | semidirect |
| 131. C97 | #1876 | semidirect |
| 138. #336 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690816 | 2 |
| C2×#15690738 | 2 |
| #20260701 | 2 |
| #20260500 | 2 |
| #336×C97 | 2 |
| #1876 | 97 |