Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
822 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. #20241515 | C2 | semidirect |
| 4. #20241514 | C2 | semidirect |
| 5. C47×#1394 | C2 | semidirect |
| 11. #15689106 | C4 | semidirect |
| 48. #13093943 | C2×C4 | semidirect |
| 56. #101×C47 | C2×C4 | semidirect |
| 198. #1394 | D47 | semidirect |
| 221. C47 | #12585 | semidirect |
| 255. #101 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689106 | 2 |
| #20245877 | 2 |
| #20241515 | 2 |
| #20241514 | 2 |
| C47×#1394 | 2 |
| #12585 | 47 |