Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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. #20243006 | C2 | semidirect |
| 4. #20243005 | C2 | semidirect |
| 5. #20243004 | C2 | semidirect |
| 7. C47×#1713 | C2 | semidirect |
| 67. C8×D47 | Q16 | semidirect |
| 82. C8×C47 | C2×Q16 | semidirect |
| 84. C47⋊C8 | C2×Q16 | semidirect |
| 100. #1713 | D47 | direct (N × H) |
| 104. D47 | #1713 | direct (N × H) |
| 121. C47 | C2×#1713 | semidirect |
| 182. C8 | Q16×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D47 | 2 |
| #494×D47 | 2 |
| #20243006 | 2 |
| #20243005 | 2 |
| #20243004 | 2 |
| C82×D47 | 2 |
| C47×#1713 | 2 |
| C2×#1713 | 47 |