Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1088 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 317 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×#15690717 | C2 | semidirect |
| 7. C2×C22⋊Dic97 | C4 | semidirect |
| 12. C23×C4×C97 | C4 | semidirect |
| 18. C22×Dic97 | C2×C4 | semidirect |
| 58. C2×C4×C97 | C22⋊C4 | semidirect |
| 70. C22×C97 | #95 | semidirect |
| 94. C97 | C22⋊#95 | semidirect |
| 102. C23×C4 | Dic97 | semidirect |
| 157. C2×C4 | C22⋊Dic97 | semidirect |
| 164. C22 | #15690717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic97 | 2 |
| C2×#15690717 | 2 |
| C24×C4×C97 | 2 |
| C22⋊#95 | 97 |