Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
414 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C4⋊C16×D47 | C2 | semidirect |
| 3. #20242135 | C2 | semidirect |
| 4. #20241438 | C2 | semidirect |
| 5. #20241436 | C2 | semidirect |
| 6. #20241434 | C2 | semidirect |
| 7. C47×#1361 | C2 | semidirect |
| 147. #1361 | D47 | semidirect |
| 170. C47 | #11929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253815 | 2 |
| C4⋊C16×D47 | 2 |
| #20242135 | 2 |
| #20241438 | 2 |
| #20241436 | 2 |
| #20241434 | 2 |
| C47×#1361 | 2 |
| #11929 | 47 |