Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15690775 | C2 | semidirect |
| 4. #20260832 | C2 | direct (N × H) |
| 5. C2×#15690743 | C2 | semidirect |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#15690720 | C2 | semidirect |
| 11. C2×#13095499 | C4 | semidirect |
| 15. #15690775 | C22 | semidirect |
| 23. #15690743 | C22 | semidirect |
| 24. #15690735 | C22 | semidirect |
| 25. #15690720 | C22 | semidirect |
| 32. C2×Dic194 | C2×C4 | semidirect |
| 40. #13095499 | C2×C4 | semidirect |
| 41. C2×#11715895 | C2×C4 | semidirect |
| 86. Dic194 | C22×C4 | semidirect |
| 88. #11715895 | C22×C4 | semidirect |
| 106. C2×C97 | #440 | semidirect |
| 111. C97 | C2×#440 | semidirect |
| 217. C2 | #20260832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C2×#15690775 | 2 |
| C2×D4×Dic97 | 2 |
| #20260832 | 2 |
| C2×#15690743 | 2 |
| C2×#15690735 | 2 |
| C2×#15690720 | 2 |
| C2×#102×C97 | 2 |
| C2×#440 | 97 |