Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
760 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 407 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×C4×#11715906 | C2 | direct (N × H) |
| 4. C22×#11715906 | C4 | direct (N × H) |
| 6. C4×#11715906 | C22 | direct (N × H) |
| 12. C2×#11715906 | C2×C4 | direct (N × H) |
| 14. C22×#87604 | C8 | semidirect |
| 22. C22×Dic97 | C8 | semidirect |
| 23. C2×C4×D97 | C8 | semidirect |
| 25. C22×C4×C97 | C8 | semidirect |
| 32. C2×#87604 | C2×C8 | semidirect |
| 37. #11715906 | C22×C4 | direct (N × H) |
| 38. C2×C4×C97 | C2×C8 | semidirect |
| 39. C2×Dic97 | C2×C8 | semidirect |
| 40. C4×D97 | C2×C8 | semidirect |
| 42. C22×C97 | C4×C8 | semidirect |
| 44. C2×D97 | C4×C8 | semidirect |
| 50. #87604 | C22×C8 | semidirect |
| 52. C4×C97 | C22×C8 | semidirect |
| 53. Dic97 | C22×C8 | semidirect |
| 54. C2×C97 | C2×C4×C8 | semidirect |
| 56. D97 | C2×C4×C8 | semidirect |
| 60. C97 | C22×C4×C8 | semidirect |
| 81. C22×C4 | #11715906 | direct (N × H) |
| 100. C2×C4 | C2×#11715906 | direct (N × H) |
| 107. C22 | C4×#11715906 | direct (N × H) |
| 113. C4 | C22×#11715906 | direct (N × H) |
| 117. C2 | C2×C4×#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| C22×C4×#87604 | 2 |
| C22×C4×C8 | 97 |