Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 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. #20243434 | C2 | semidirect |
| 4. #20241508 | C2 | semidirect |
| 5. C47×#1812 | C2 | semidirect |
| 6. C2×#13094030 | C4 | semidirect |
| 13. #15689146 | C4 | semidirect |
| 15. #15689091 | C4 | semidirect |
| 17. C2×C8×Dic47 | C4 | semidirect |
| 183. #1812 | D47 | semidirect |
| 210. C47 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252098 | 2 |
| #20245051 | 2 |
| #20243434 | 2 |
| #20241508 | 2 |
| C47×#1812 | 2 |
| #12807 | 47 |