Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20243571 | C2 | semidirect |
| 4. #20241908 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1901 | C2 | semidirect |
| 215. #1901 | D47 | semidirect |
| 252. C47 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254141 | 2 |
| #20243851 | 2 |
| #20243571 | 2 |
| #20241908 | 2 |
| #20241905 | 2 |
| #20241264 | 2 |
| C47×#1901 | 2 |
| #10558 | 47 |