Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245645 | C2 | semidirect |
| 3. #20245435 | C2 | semidirect |
| 4. #20241433 | C2 | semidirect |
| 5. #20241351 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. C47×#1669 | C2 | semidirect |
| 144. #1669 | D47 | semidirect |
| 170. C47 | #12321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255148 | 2 |
| #20245645 | 2 |
| #20245435 | 2 |
| #20241433 | 2 |
| #20241351 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#1669 | 2 |
| #12321 | 47 |