Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
2488 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1106 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. C22×C4⋊#87604 | C2 | direct (N × H) |
| 6. C2×C4⋊#87604 | C22 | direct (N × H) |
| 8. C23×Dic97 | C4 | semidirect |
| 9. C22×C4×D97 | C4 | semidirect |
| 11. C23×C4×C97 | C4 | semidirect |
| 14. C4⋊#87604 | C23 | direct (N × H) |
| 19. C22×Dic97 | C2×C4 | semidirect |
| 20. C2×C4×D97 | C2×C4 | semidirect |
| 23. C22×C4×C97 | C2×C4 | semidirect |
| 24. C23×C97 | C4⋊C4 | semidirect |
| 26. C22×D97 | C4⋊C4 | semidirect |
| 33. C2×C4×C97 | C22×C4 | semidirect |
| 34. C2×Dic97 | C22×C4 | semidirect |
| 35. C4×D97 | C22×C4 | semidirect |
| 37. C22×C97 | C2×C4⋊C4 | semidirect |
| 39. C2×D97 | C2×C4⋊C4 | semidirect |
| 45. C4×C97 | C23×C4 | semidirect |
| 46. Dic97 | C23×C4 | semidirect |
| 47. C2×C97 | C22×C4⋊C4 | semidirect |
| 49. D97 | C22×C4⋊C4 | semidirect |
| 53. C97 | C23×C4⋊C4 | semidirect |
| 63. C23×C4 | #87604 | semidirect |
| 75. C22×C4 | C2×#87604 | semidirect |
| 82. C23 | C4⋊#87604 | direct (N × H) |
| 89. C2×C4 | C22×#87604 | semidirect |
| 95. C22 | C2×C4⋊#87604 | direct (N × H) |
| 99. C4 | C23×#87604 | semidirect |
| 103. C2 | C22×C4⋊#87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#87604 | 2 |
| C22×C4⋊#87604 | 2 |
| C23×C4×D97 | 2 |
| C23×C4⋊C4 | 97 |