Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1164 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20256790 | C2 | semidirect |
| 3. #20244566 | C2 | semidirect |
| 4. #20244565 | C2 | semidirect |
| 5. #20244564 | C2 | semidirect |
| 6. #20243119 | C2 | semidirect |
| 7. C47×#2032 | C2 | semidirect |
| 29. C22×Dic94 | Q8 | semidirect |
| 30. C22×C22⋊D47 | Q8 | semidirect |
| 32. C23×Dic47 | Q8 | semidirect |
| 34. C22×C4×D47 | Q8 | semidirect |
| 187. #2032 | D47 | semidirect |
| 212. C47 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256790 | 2 |
| C2×#15689095 | 2 |
| #20244566 | 2 |
| #20244565 | 2 |
| #20244564 | 2 |
| #20243119 | 2 |
| C47×#2032 | 2 |
| #23474 | 47 |