Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690840 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. #20261212 | C2 | semidirect |
| 4. #20260954 | C2 | semidirect |
| 5. #20260932 | C2 | semidirect |
| 6. #20260762 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 15. C2×#13095499 | C22 | semidirect |
| 18. C4×Dic194 | C22 | semidirect |
| 22. C4⋊#11715895 | C22 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 25. #15690731 | C22 | semidirect |
| 35. C2×Dic194 | D4 | semidirect |
| 117. C97 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C22×#13095499 | 2 |
| #20261212 | 2 |
| #20260954 | 2 |
| #20260932 | 2 |
| #20260762 | 2 |
| #20260740 | 2 |
| #20260731 | 2 |
| #535×C97 | 2 |
| #3043 | 97 |