Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#15689566 | C2 | semidirect |
| 3. C2×#15689507 | C2 | semidirect |
| 4. C2×#15688940 | C2 | semidirect |
| 5. C2×#15688937 | C2 | semidirect |
| 6. #20244276 | C2 | semidirect |
| 7. C47×#1376 | C2 | semidirect |
| 199. #1376 | D47 | semidirect |
| 229. C47 | #13332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689566 | 2 |
| C2×#15689561 | 2 |
| C2×#15689507 | 2 |
| C2×#15688940 | 2 |
| C2×#15688937 | 2 |
| #20244276 | 2 |
| C47×#1376 | 2 |
| #13332 | 47 |