Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 242 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. #20261752 | C2 | direct (N × H) |
| 2. C2×#15690877 | C2 | semidirect |
| 4. C2×C4×#11715897 | C2 | semidirect |
| 7. #15690877 | C22 | semidirect |
| 9. C4×#11715897 | C22 | semidirect |
| 22. C22×Dic97 | C8 | semidirect |
| 56. C2×Dic97 | C2×C8 | semidirect |
| 80. C2×C97 | #431 | semidirect |
| 85. C97 | C2×#431 | semidirect |
| 165. C2 | #20261752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261752 | 2 |
| C2×#15690877 | 2 |
| C2×C22⋊#11715897 | 2 |
| C2×C4×#11715897 | 2 |
| C22×C4×Dic97 | 2 |
| C2×#431 | 97 |