Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20261857 | C2 | semidirect |
| 2. #20261856 | C2 | semidirect |
| 3. #20261840 | C2 | semidirect |
| 4. #20261836 | C2 | semidirect |
| 5. #20261835 | C2 | semidirect |
| 6. #20261830 | C2 | semidirect |
| 72. C97 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261857 | 2 |
| #20261856 | 2 |
| #20261840 | 2 |
| #20261836 | 2 |
| #20261835 | 2 |
| #20261830 | 2 |
| #20261778 | 2 |
| #2171 | 97 |