Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
774 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 206 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. C2×#15690898 | C2 | semidirect |
| 2. #20261710 | C2 | semidirect |
| 3. #20261706 | C2 | semidirect |
| 4. #20261703 | C2 | semidirect |
| 7. C2×#13095521 | C22 | semidirect |
| 8. C2×#13095519 | C22 | semidirect |
| 9. #15690867 | C22 | semidirect |
| 10. #15690867 | C22 | semidirect |
| 69. C22×C97 | #131 | semidirect |
| 89. C97 | #2880 | semidirect |
| 165. C22 | #15690898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261710 | 2 |
| #20261706 | 2 |
| #20261703 | 2 |
| C22×#13095512 | 2 |
| #2880 | 97 |