Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20261209 | C2 | semidirect |
| 3. #20260848 | C2 | semidirect |
| 4. C4×D776 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260741 | C2 | semidirect |
| 7. #405×C97 | C2 | semidirect |
| 9. C2×D776 | C4 | semidirect |
| 12. C4×D388 | C22 | semidirect |
| 16. #15690744 | C22 | semidirect |
| 17. #15690742 | C22 | semidirect |
| 18. #15690732 | C22 | semidirect |
| 22. #97×C97 | C22 | semidirect |
| 23. C4×C8×C97 | C22 | semidirect |
| 27. C2×D388 | C2×C4 | semidirect |
| 30. D776 | C2×C4 | semidirect |
| 31. D776 | C2×C4 | semidirect |
| 38. C2×C8×C97 | C2×C4 | semidirect |
| 78. C97 | #2948 | semidirect |
| 85. #405 | D97 | semidirect |
| 100. #97 | C2×D97 | semidirect |
| 101. C4×C8 | C2×D97 | semidirect |
| 112. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| #20261209 | 2 |
| #20260848 | 2 |
| C4×D776 | 2 |
| #20260773 | 2 |
| #20260741 | 2 |
| #405×C97 | 2 |
| #2948 | 97 |