Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
640 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 378 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⋊#11715897 | C2 | direct (N × H) |
| 6. C4⋊#11715897 | C22 | direct (N × H) |
| 23. C22×C4×C97 | C8 | semidirect |
| 29. C2×C4×C97 | C2×C8 | semidirect |
| 39. C22×C97 | C4⋊C8 | semidirect |
| 44. C4×C97 | C22×C8 | semidirect |
| 49. C2×C97 | C2×C4⋊C8 | semidirect |
| 54. C97 | C22×C4⋊C8 | semidirect |
| 73. C22×C4 | #11715897 | semidirect |
| 90. C2×C4 | C2×#11715897 | semidirect |
| 93. C22 | C4⋊#11715897 | direct (N × H) |
| 102. C4 | C22×#11715897 | semidirect |
| 103. C2 | C2×C4⋊#11715897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715897 | 2 |
| C2×C4⋊#11715897 | 2 |
| C22×C4×Dic97 | 2 |
| C22×C4⋊C8 | 97 |