Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
984 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 255 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. #20243679 | C2 | semidirect |
| 3. #20243531 | C2 | semidirect |
| 4. C47×#1839 | C2 | semidirect |
| 18. #13094021 | C8 | semidirect |
| 35. C2×D188 | C2×C8 | semidirect |
| 41. C42×C47 | C2×C8 | semidirect |
| 76. #1839 | D47 | semidirect |
| 90. C47 | #23355 | semidirect |
| 122. C42 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13094021 | 2 |
| #20243679 | 2 |
| #20243531 | 2 |
| C47×#1839 | 2 |
| #23355 | 47 |