Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 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 |
|---|---|---|
| 1. #20261210 | C2 | direct (N × H) |
| 2. C2×D4×Dic97 | C2 | semidirect |
| 3. C2×#15690769 | C2 | semidirect |
| 4. C22×C22⋊Dic97 | C2 | semidirect |
| 6. C23×Dic97 | C22 | semidirect |
| 7. D4×Dic97 | C22 | semidirect |
| 8. #15690769 | C22 | semidirect |
| 9. C2×C4⋊Dic97 | C22 | semidirect |
| 11. C2×C22⋊Dic97 | C22 | semidirect |
| 12. C2×C22⋊Dic97 | C22 | semidirect |
| 13. C2×C4×Dic97 | C22 | semidirect |
| 15. C22×D4×C97 | C4 | semidirect |
| 21. C22×Dic97 | C23 | semidirect |
| 22. C4⋊Dic97 | C23 | semidirect |
| 24. C22⋊Dic97 | C23 | semidirect |
| 25. C4×Dic97 | C23 | semidirect |
| 27. C24×C97 | C2×C4 | semidirect |
| 31. C2×D4×C97 | C2×C4 | semidirect |
| 32. C2×D4×C97 | C2×C4 | semidirect |
| 34. C22×C4×C97 | C2×C4 | semidirect |
| 43. C23×C97 | C22×C4 | semidirect |
| 47. D4×C97 | C22×C4 | semidirect |
| 49. C2×C4×C97 | C22×C4 | semidirect |
| 68. C2×C97 | #518 | semidirect |
| 72. C97 | C2×#518 | semidirect |
| 79. C22×D4 | Dic97 | semidirect |
| 92. C24 | C2×Dic97 | semidirect |
| 96. C2×D4 | C2×Dic97 | semidirect |
| 97. C2×D4 | C2×Dic97 | semidirect |
| 102. C22×C4 | C2×Dic97 | semidirect |
| 115. C23 | C22×Dic97 | semidirect |
| 119. D4 | C22×Dic97 | semidirect |
| 124. C2×C4 | C22×Dic97 | semidirect |
| 140. C2 | #20261210 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261210 | 2 |
| C2×D4×Dic97 | 2 |
| C2×#15690769 | 2 |
| C22×C22⋊Dic97 | 2 |
| C23×D4×C97 | 2 |
| C2×#518 | 97 |