Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261087 | C2 | semidirect |
| 2. #20261086 | C2 | semidirect |
| 3. #20261085 | C2 | semidirect |
| 6. C8×#11715895 | C2 | semidirect |
| 68. C97 | #1711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261087 | 2 |
| #20261086 | 2 |
| #20261085 | 2 |
| #20261081 | 2 |
| C8×#11715895 | 2 |
| #486×C97 | 2 |
| #1711 | 97 |