Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20253910 | C2 | semidirect |
| 5. #20241951 | C2 | semidirect |
| 6. #20241232 | C2 | semidirect |
| 7. C47×#1518 | C2 | semidirect |
| 121. C2×C47⋊C8 | SD16 | semidirect |
| 186. #1518 | D47 | semidirect |
| 217. C47 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254331 | 2 |
| #20254326 | 2 |
| #20253910 | 2 |
| #20244211 | 2 |
| #20241951 | 2 |
| #20241232 | 2 |
| C47×#1518 | 2 |
| #10220 | 47 |