Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20257788 | C2 | semidirect |
| 2. #20254379 | C2 | semidirect |
| 3. #20242709 | C2 | semidirect |
| 4. #20242680 | C2 | semidirect |
| 5. #20242026 | C2 | semidirect |
| 6. #20241998 | C2 | semidirect |
| 7. C47×#3135 | C2 | semidirect |
| 160. #3135 | 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 |
|---|---|
| #20257788 | 2 |
| #20254379 | 2 |
| #20242709 | 2 |
| #20242680 | 2 |
| #20242026 | 2 |
| #20241998 | 2 |
| C47×#3135 | 2 |
| #19061 | 47 |