Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
640 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 287 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) |
| 6. C4⋊#11715906 | C22 | direct (N × H) |
| 23. C22×Dic97 | C8 | semidirect |
| 24. C2×C4×D97 | C8 | semidirect |
| 26. C22×C4×C97 | C8 | semidirect |
| 40. C2×C4×C97 | C2×C8 | semidirect |
| 41. C2×Dic97 | C2×C8 | semidirect |
| 42. C4×D97 | C2×C8 | semidirect |
| 44. C22×C97 | C4⋊C8 | semidirect |
| 46. C2×D97 | C4⋊C8 | semidirect |
| 55. C4×C97 | C22×C8 | semidirect |
| 56. Dic97 | C22×C8 | semidirect |
| 57. C2×C97 | C2×C4⋊C8 | semidirect |
| 59. D97 | C2×C4⋊C8 | semidirect |
| 63. C97 | C22×C4⋊C8 | semidirect |
| 85. C22×C4 | #11715906 | semidirect |
| 105. C2×C4 | C2×#11715906 | semidirect |
| 112. C22 | C4⋊#11715906 | direct (N × H) |
| 119. C4 | C22×#11715906 | semidirect |
| 123. 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 |