Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20261700 | C2 | semidirect |
| 4. C2×#15690864 | C2 | semidirect |
| 5. #20261611 | C2 | semidirect |
| 6. #20261605 | C2 | semidirect |
| 9. #15690898 | C4 | semidirect |
| 16. #15690875 | C4 | semidirect |
| 23. #15690734 | C4 | semidirect |
| 24. #15690732 | C4 | semidirect |
| 25. #15690730 | C4 | semidirect |
| 26. #103×C97 | C4 | semidirect |
| 110. C97 | #1765 | semidirect |
| 131. #103 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| C2×#15690875 | 2 |
| #20261700 | 2 |
| C2×#15690864 | 2 |
| #20261611 | 2 |
| #20261605 | 2 |
| #20260730 | 2 |
| #1765 | 97 |