Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#15690720 | C2 | semidirect |
| 5. C2×C8×Dic97 | C2 | semidirect |
| 6. #20260490 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 16. #15690722 | C4 | semidirect |
| 17. #15690722 | C4 | semidirect |
| 105. C97 | #1750 | semidirect |
| 112. #336 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690767 | 2 |
| C2×#15690722 | 2 |
| C2×#15690720 | 2 |
| C2×C8×Dic97 | 2 |
| #20260490 | 2 |
| #336×C97 | 2 |
| #1750 | 97 |