Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
942 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #20254383 | C2 | semidirect |
| 2. #20253736 | C2 | semidirect |
| 3. #20242711 | C2 | semidirect |
| 4. #20242681 | C2 | semidirect |
| 5. #20242026 | C2 | semidirect |
| 6. #20241999 | C2 | semidirect |
| 7. C47×#3548 | C2 | semidirect |
| 158. #3548 | D47 | semidirect |
| 192. C47 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254383 | 2 |
| #20253736 | 2 |
| #20242711 | 2 |
| #20242681 | 2 |
| #20242026 | 2 |
| #20241999 | 2 |
| C47×#3548 | 2 |
| #19061 | 47 |