Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
212 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #20261595 | C2 | semidirect |
| 4. #20261594 | C2 | semidirect |
| 89. C97 | #1542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261752 | 2 |
| C2×#15690877 | 2 |
| #20261595 | 2 |
| #20261594 | 2 |
| #20261287 | 2 |
| #1542 | 97 |