Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20251978 | C2 | semidirect |
| 3. #20245105 | C2 | semidirect |
| 4. #20241494 | C2 | semidirect |
| 5. C2×C47×#349 | C2 | semidirect |
| 10. #15689376 | C4 | semidirect |
| 25. C2×D376 | C2×C4 | semidirect |
| 38. #13093958 | D4 | semidirect |
| 42. #13093956 | C2×C4 | semidirect |
| 154. C2×#349 | D47 | semidirect |
| 176. C47 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689376 | 2 |
| #20251978 | 2 |
| #20245105 | 2 |
| #20241494 | 2 |
| C2×C47×#349 | 2 |
| #12999 | 47 |