Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic388 | C2 | semidirect |
| 2. #20261175 | C2 | direct (N × H) |
| 3. C2×#15690756 | C2 | semidirect |
| 4. C2×#15690754 | C2 | semidirect |
| 5. C2×#15690750 | C2 | semidirect |
| 11. C2×Dic388 | C22 | semidirect |
| 12. #15690756 | C22 | semidirect |
| 13. #15690754 | C22 | semidirect |
| 14. #15690750 | C22 | semidirect |
| 81. C2×C97 | #510 | semidirect |
| 84. C97 | C2×#510 | semidirect |
| 165. C2 | #20261175 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic388 | 2 |
| #20261175 | 2 |
| C2×#15690756 | 2 |
| C2×#15690754 | 2 |
| C2×#15690750 | 2 |
| C2×#135×C97 | 2 |
| C2×#510 | 97 |