Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
33214 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3307 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. C23×C22⋊Dic47 | C2 | semidirect |
| 2. C2×#15688979 | C2 | direct (N × H) |
| 4. C24×Dic47 | C22 | semidirect |
| 6. C22×C22⋊Dic47 | C22 | semidirect |
| 7. #15688979 | C22 | direct (N × H) |
| 9. C26×C47 | C4 | semidirect |
| 13. C23×Dic47 | C23 | semidirect |
| 15. C2×C22⋊Dic47 | C23 | semidirect |
| 21. C25×C47 | C2×C4 | semidirect |
| 33. C24×C47 | C22⋊C4 | semidirect |
| 36. C24×C47 | C22×C4 | semidirect |
| 43. C22×Dic47 | C24 | semidirect |
| 53. C23×C47 | C2×C22⋊C4 | semidirect |
| 67. C22×C47 | #379 | semidirect |
| 69. C22×C47 | C22×C22⋊C4 | semidirect |
| 78. C2×C47 | C2×#379 | semidirect |
| 82. C26 | Dic47 | semidirect |
| 89. C47 | C22×#379 | semidirect |
| 95. C25 | C2×Dic47 | semidirect |
| 111. C24 | C22⋊Dic47 | semidirect |
| 114. C24 | C22×Dic47 | semidirect |
| 131. C23 | C2×C22⋊Dic47 | semidirect |
| 144. C22 | #15688979 | direct (N × H) |
| 146. C22 | C22×C22⋊Dic47 | semidirect |
| 152. C2 | C2×#15688979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Dic47 | 2 |
| C2×#15688979 | 2 |
| C27×C47 | 2 |
| C22×#379 | 47 |