Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20261656 | C2 | semidirect |
| 3. #20261623 | C2 | semidirect |
| 58. C97 | #2163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261656 | 2 |
| #20261630 | 2 |
| #20261623 | 2 |
| C4×C8×D97 | 2 |
| #2163 | 97 |