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 |
|---|---|---|
| 2. C2×#15690745 | C2 | semidirect |
| 3. #20260771 | C2 | semidirect |
| 6. #20260507 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 11. #15690818 | C4 | semidirect |
| 12. #15690818 | C4 | semidirect |
| 106. C97 | #1814 | semidirect |
| 113. #344 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690818 | 2 |
| C2×#15690745 | 2 |
| #20260771 | 2 |
| #20260753 | 2 |
| #20260751 | 2 |
| #20260507 | 2 |
| #344×C97 | 2 |
| #1814 | 97 |