Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
294 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #20241450 | C2 | semidirect |
| 5. #20241449 | C2 | semidirect |
| 6. #20241448 | C2 | semidirect |
| 7. C47×#1366 | C2 | semidirect |
| 121. #1366 | D47 | direct (N × H) |
| 125. D47 | #1366 | direct (N × H) |
| 143. C47 | C2×#1366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D47 | 2 |
| #364×D47 | 2 |
| #20241450 | 2 |
| #20241449 | 2 |
| #20241448 | 2 |
| C47×#1366 | 2 |
| C2×#1366 | 47 |