Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20246113 | C2 | semidirect |
| 3. #20242057 | C2 | semidirect |
| 4. #20241948 | C2 | semidirect |
| 5. #20241248 | C2 | semidirect |
| 6. #20241217 | C2 | semidirect |
| 7. C47×#1963 | C2 | semidirect |
| 10. #15689499 | C4 | semidirect |
| 11. #15689471 | C4 | semidirect |
| 48. C4×C47⋊C8 | C2×C4 | semidirect |
| 53. C4⋊Q8×C47 | C2×C4 | semidirect |
| 54. #127×C47 | C2×C4 | semidirect |
| 111. C42×C47 | D8 | semidirect |
| 207. #1963 | D47 | semidirect |
| 238. C47 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D47 | semidirect |
| 251. #127 | C4×D47 | semidirect |
| 331. C42 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254303 | 2 |
| #20246113 | 2 |
| #20242057 | 2 |
| #20241948 | 2 |
| #20241248 | 2 |
| #20241217 | 2 |
| C47×#1963 | 2 |
| #9299 | 47 |