Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#15690864 | C2 | semidirect |
| 4. C2×C8×#87604 | C2 | semidirect |
| 5. #20261600 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 16. #15690867 | C4 | semidirect |
| 17. C22⋊#11715897 | C4 | semidirect |
| 23. C22⋊#11715895 | C4 | semidirect |
| 24. #15690722 | C4 | semidirect |
| 25. #15690722 | C4 | semidirect |
| 26. C22⋊C8×C97 | C4 | semidirect |
| 126. C97 | #1750 | semidirect |
| 150. C22⋊C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261703 | 2 |
| C2×#15690864 | 2 |
| C2×C8×#87604 | 2 |
| #20261600 | 2 |
| C22⋊C8×D97 | 2 |
| #1750 | 97 |