Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20246296 | C2 | semidirect |
| 3. #20241883 | C2 | semidirect |
| 4. #20241780 | C2 | semidirect |
| 5. #20241290 | C2 | semidirect |
| 6. #20241246 | C2 | semidirect |
| 7. C47×#1517 | C2 | semidirect |
| 12. #15689325 | C4 | semidirect |
| 13. #15689315 | C4 | semidirect |
| 51. C4⋊(C47⋊C8) | C2×C4 | semidirect |
| 60. C4⋊Q8×C47 | C2×C4 | semidirect |
| 61. #127×C47 | C2×C4 | semidirect |
| 210. #1517 | D47 | semidirect |
| 243. C47 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D47 | semidirect |
| 254. #127 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252848 | 2 |
| #20246296 | 2 |
| #20241883 | 2 |
| #20241780 | 2 |
| #20241290 | 2 |
| #20241246 | 2 |
| C47×#1517 | 2 |
| #9179 | 47 |