Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20256524 | C2 | semidirect |
| 2. C2×#15689561 | C2 | semidirect |
| 3. #20253874 | C2 | semidirect |
| 4. #20245125 | C2 | semidirect |
| 5. #20245105 | C2 | semidirect |
| 6. #20244286 | C2 | semidirect |
| 7. C47×#1378 | C2 | semidirect |
| 47. C2×Dic188 | D4 | semidirect |
| 59. C2×D376 | D4 | semidirect |
| 81. M32×C47 | D4 | semidirect |
| 83. C2×C16×C47 | D4 | semidirect |
| 217. #1378 | D47 | semidirect |
| 250. C47 | #13334 | semidirect |
| 295. M32 | D188 | semidirect |
| 297. C2×C16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256524 | 2 |
| C2×#15689561 | 2 |
| #20253874 | 2 |
| #20245125 | 2 |
| #20245105 | 2 |
| #20244286 | 2 |
| C47×#1378 | 2 |
| #13334 | 47 |