Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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. #20253947 | C2 | semidirect |
| 2. #20253902 | C2 | semidirect |
| 4. #20243021 | C2 | semidirect |
| 5. #20243016 | C2 | semidirect |
| 6. #20243010 | C2 | semidirect |
| 7. C2×C47×#322 | C2 | semidirect |
| 68. C2×C8×C47 | SD16 | semidirect |
| 123. C2×#322 | D47 | semidirect |
| 149. C47 | #19608 | semidirect |
| 193. C2×C8 | #10625325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253947 | 2 |
| #20253902 | 2 |
| #20253816 | 2 |
| #20243021 | 2 |
| #20243016 | 2 |
| #20243010 | 2 |
| C2×C47×#322 | 2 |
| #19608 | 47 |