Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
912 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20254331 | C2 | semidirect |
| 2. #20254329 | C2 | semidirect |
| 4. #20244364 | C2 | semidirect |
| 5. #20242057 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1545 | C2 | semidirect |
| 35. #13094024 | D4 | semidirect |
| 36. #13094024 | D4 | semidirect |
| 54. C4⋊(C47⋊C8) | D4 | semidirect |
| 70. C4⋊C8×C47 | D4 | semidirect |
| 123. C4×Dic47 | SD16 | semidirect |
| 198. #1545 | D47 | semidirect |
| 227. C47 | #10290 | semidirect |
| 265. C4⋊C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254331 | 2 |
| #20254329 | 2 |
| #20251782 | 2 |
| #20244364 | 2 |
| #20242057 | 2 |
| #20241220 | 2 |
| C47×#1545 | 2 |
| #10290 | 47 |