Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20252265 | C2 | semidirect |
| 3. C2×#15688931 | C2 | semidirect |
| 4. C2×#15688925 | C2 | semidirect |
| 5. #20244298 | C2 | semidirect |
| 6. #20241497 | C2 | semidirect |
| 7. C47×#1379 | C2 | semidirect |
| 12. #15689561 | C4 | semidirect |
| 41. C2×D376 | C2×C4 | semidirect |
| 65. M32×C47 | C2×C4 | semidirect |
| 188. #1379 | D47 | semidirect |
| 216. C47 | #13022 | semidirect |
| 245. M32 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689561 | 2 |
| #20252265 | 2 |
| C2×#15688931 | 2 |
| C2×#15688925 | 2 |
| #20244298 | 2 |
| #20241497 | 2 |
| C47×#1379 | 2 |
| #13022 | 47 |