Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
464 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 464 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. #20243593 | C2 | semidirect |
| 5. #20241752 | C2 | semidirect |
| 6. #20241294 | C2 | semidirect |
| 7. C47×#1894 | C2 | semidirect |
| 209. #1894 | D47 | semidirect |
| 243. C47 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254190 | 2 |
| #20243851 | 2 |
| #20243593 | 2 |
| #20241955 | 2 |
| #20241752 | 2 |
| #20241294 | 2 |
| C47×#1894 | 2 |
| #10562 | 47 |