Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20242146 | C2 | semidirect |
| 5. C2×Q8⋊(C47⋊C8) | C2 | semidirect |
| 6. #20241262 | C2 | semidirect |
| 7. C47×#1801 | C2 | semidirect |
| 184. #1801 | D47 | semidirect |
| 217. C47 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252860 | 2 |
| #20242146 | 2 |
| #20242066 | 2 |
| #20241838 | 2 |
| C2×Q8⋊(C47⋊C8) | 2 |
| #20241262 | 2 |
| C47×#1801 | 2 |
| #10458 | 47 |