Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20254705 | C2 | semidirect |
| 2. #20253488 | C2 | semidirect |
| 4. #20244185 | C2 | semidirect |
| 5. #20242004 | C2 | semidirect |
| 6. #20242000 | C2 | semidirect |
| 7. C47×#1290 | C2 | semidirect |
| 207. #1290 | D47 | semidirect |
| 239. C47 | #10027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254705 | 2 |
| #20253488 | 2 |
| #20253480 | 2 |
| #20244185 | 2 |
| #20242004 | 2 |
| #20242000 | 2 |
| C47×#1290 | 2 |
| #10027 | 47 |