Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20245221 | C2 | semidirect |
| 2. #20242750 | C2 | semidirect |
| 4. #20241460 | C2 | semidirect |
| 5. #20241437 | C2 | semidirect |
| 6. #20241434 | C2 | semidirect |
| 7. C47×#2248 | C2 | semidirect |
| 72. C16×C47 | D8 | semidirect |
| 113. #2248 | D47 | semidirect |
| 140. C47 | #12435 | semidirect |
| 191. C16 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245221 | 2 |
| #20242750 | 2 |
| #20242740 | 2 |
| #20241460 | 2 |
| #20241437 | 2 |
| #20241434 | 2 |
| C47×#2248 | 2 |
| #12435 | 47 |