Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20253963 | C2 | semidirect |
| 2. #20253816 | C2 | semidirect |
| 3. #20243060 | C2 | semidirect |
| 4. #20243057 | C2 | semidirect |
| 5. #20243055 | C2 | semidirect |
| 6. #20243052 | C2 | semidirect |
| 7. C2×#15688844 | C2 | semidirect |
| 8. C47×#3147 | C2 | semidirect |
| 80. C2×C8×C47 | D8 | semidirect |
| 136. #3147 | D47 | semidirect |
| 169. C47 | #19616 | semidirect |
| 225. C2×C8 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253963 | 2 |
| #20253816 | 2 |
| #20243060 | 2 |
| #20243057 | 2 |
| #20243055 | 2 |
| #20243052 | 2 |
| C2×#15688844 | 2 |
| C47×#3147 | 2 |
| #19616 | 47 |