Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1036 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 261 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. C23×Dic194 | C2 | semidirect |
| 3. #20260647 | C2 | direct (N × H) |
| 4. C2×#15690717 | C2 | semidirect |
| 5. C2×#15690717 | C2 | semidirect |
| 9. C22×Dic194 | C22 | semidirect |
| 14. #15690717 | C22 | semidirect |
| 15. #15690717 | C22 | semidirect |
| 37. C24×C97 | Q8 | semidirect |
| 59. C23×C97 | C2×Q8 | semidirect |
| 99. C2×C97 | #393 | semidirect |
| 106. C97 | C2×#393 | semidirect |
| 131. C24 | Dic194 | semidirect |
| 165. C23 | C2×Dic194 | semidirect |
| 205. C2 | #20260647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic194 | 2 |
| C22×C22⋊Dic97 | 2 |
| #20260647 | 2 |
| C2×#15690717 | 2 |
| C22×C22⋊C4×C97 | 2 |
| C2×#393 | 97 |