Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #20261502 | C2 | semidirect |
| 3. #20260717 | C2 | semidirect |
| 4. C2×#15690728 | C2 | semidirect |
| 5. #568×C97 | C2 | semidirect |
| 75. C97 | #2889 | semidirect |
| 78. #568 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| #20261502 | 2 |
| #20260717 | 2 |
| C2×#15690728 | 2 |
| #568×C97 | 2 |
| #2889 | 97 |