Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20261212 | C2 | semidirect |
| 3. #20260835 | C2 | semidirect |
| 4. C4×#13095499 | C2 | semidirect |
| 5. #20260771 | C2 | semidirect |
| 6. #20260743 | C2 | semidirect |
| 8. #20260691 | C2 | semidirect |
| 11. C2×#13095499 | C4 | semidirect |
| 16. C4×Dic194 | C22 | semidirect |
| 20. #15690743 | C22 | semidirect |
| 21. #15690741 | C22 | semidirect |
| 22. #15690733 | C22 | semidirect |
| 24. #15690721 | C22 | semidirect |
| 25. C4×#11715895 | C22 | semidirect |
| 34. C2×Dic194 | C2×C4 | semidirect |
| 37. #13095499 | C2×C4 | semidirect |
| 38. #13095499 | C2×C4 | semidirect |
| 40. C2×#11715895 | C2×C4 | semidirect |
| 104. C97 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| #20261212 | 2 |
| #20260835 | 2 |
| C4×#13095499 | 2 |
| #20260771 | 2 |
| #20260743 | 2 |
| #20260740 | 2 |
| #20260691 | 2 |
| #518×C97 | 2 |
| #2949 | 97 |