Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690841 | C2 | semidirect |
| 2. C2×#15690840 | C2 | semidirect |
| 4. C22×#13095501 | C2 | semidirect |
| 5. #20261311 | C2 | semidirect |
| 6. #20261130 | C2 | semidirect |
| 7. #20261127 | C2 | semidirect |
| 8. #20261117 | C2 | semidirect |
| 9. #20261114 | C2 | semidirect |
| 10. #20260691 | C2 | semidirect |
| 11. #536×C97 | C2 | semidirect |
| 144. C97 | #3156 | semidirect |
| 150. #536 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| C2×#15690840 | 2 |
| C2×#15690830 | 2 |
| C22×#13095501 | 2 |
| #20261311 | 2 |
| #20261130 | 2 |
| #20261127 | 2 |
| #20261117 | 2 |
| #20261114 | 2 |
| #20260691 | 2 |
| #536×C97 | 2 |
| #3156 | 97 |