Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20260792 | C2 | semidirect |
| 2. C2×#15690721 | C2 | semidirect |
| 3. #20260475 | C2 | semidirect |
| 81. C97 | #1530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260792 | 2 |
| C2×#15690721 | 2 |
| #20260475 | 2 |
| #532×C97 | 2 |
| #1530 | 97 |