Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20260783 | C2 | semidirect |
| 3. #20260744 | C2 | semidirect |
| 5. C2×#15690729 | C2 | semidirect |
| 6. #20260507 | C2 | semidirect |
| 106. C97 | #2049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260783 | 2 |
| #20260752 | 2 |
| #20260744 | 2 |
| #20260719 | 2 |
| C2×#15690729 | 2 |
| #20260507 | 2 |
| C2×#137×C97 | 2 |
| #2049 | 97 |