Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20256020 | C2 | semidirect |
| 2. #20255053 | C2 | semidirect |
| 3. #20242850 | C2 | semidirect |
| 4. #20242829 | C2 | semidirect |
| 5. #20242634 | C2 | semidirect |
| 6. #20242450 | C2 | semidirect |
| 7. #20242274 | C2 | semidirect |
| 8. C8×Dic188 | C2 | semidirect |
| 9. C47×#1706 | C2 | semidirect |
| 123. Dic188 | D8 | semidirect |
| 179. #1706 | D47 | semidirect |
| 220. C47 | #19888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256020 | 2 |
| #20255053 | 2 |
| #20242850 | 2 |
| #20242829 | 2 |
| #20242634 | 2 |
| #20242450 | 2 |
| #20242274 | 2 |
| C8×Dic188 | 2 |
| C47×#1706 | 2 |
| #19888 | 47 |