Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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×#15690897 | C2 | direct (N × H) |
| 2. C22×#13095521 | C2 | semidirect |
| 3. C22×#13095520 | C2 | semidirect |
| 4. C22×#13095519 | C2 | semidirect |
| 5. C23×#11715897 | C2 | semidirect |
| 7. #15690897 | C22 | direct (N × H) |
| 8. C2×#13095521 | C22 | semidirect |
| 9. C2×#13095520 | C22 | semidirect |
| 10. C2×#13095519 | C22 | semidirect |
| 14. C22×#11715897 | C22 | semidirect |
| 22. #13095521 | C23 | semidirect |
| 23. #13095520 | C23 | semidirect |
| 24. #13095519 | C23 | semidirect |
| 28. C2×#11715897 | C23 | semidirect |
| 63. C22×C97 | #131 | semidirect |
| 73. C2×C97 | C2×#131 | semidirect |
| 77. C97 | C22×#131 | semidirect |
| 142. C22 | #15690897 | direct (N × H) |
| 151. C2 | C2×#15690897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690897 | 2 |
| C22×#13095521 | 2 |
| C22×#13095520 | 2 |
| C22×#13095519 | 2 |
| C23×#11715897 | 2 |
| C22×#13095510 | 2 |
| C22×#131 | 97 |