Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20251770 | C2 | semidirect |
| 2. #20251755 | C2 | semidirect |
| 3. #20251703 | C2 | semidirect |
| 4. C4×#13094018 | C2 | semidirect |
| 6. #20245871 | C2 | semidirect |
| 7. C2×C43×C47 | C2 | semidirect |
| 65. C42×C47 | #41 | semidirect |
| 79. C2×C4×C47 | #126 | semidirect |
| 108. C2×C43 | D47 | semidirect |
| 130. C47 | #36641 | semidirect |
| 176. C42 | #10625350 | semidirect |
| 192. C2×C4 | #13094018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251770 | 2 |
| #20251755 | 2 |
| #20251703 | 2 |
| C4×#13094018 | 2 |
| #20245878 | 2 |
| #20245871 | 2 |
| C2×C43×C47 | 2 |
| #36641 | 47 |