Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #20253841 | C2 | semidirect |
| 2. #20249496 | C2 | semidirect |
| 3. #20242101 | C2 | semidirect |
| 4. #20241986 | C2 | semidirect |
| 5. #20241896 | C2 | semidirect |
| 6. #20241280 | C2 | semidirect |
| 7. C47×#3213 | C2 | semidirect |
| 50. #13093935 | D4 | semidirect |
| 59. C4⋊Q8×C47 | D4 | semidirect |
| 60. #127×C47 | D4 | semidirect |
| 73. C4⋊C8×C47 | D4 | semidirect |
| 205. #3213 | D47 | semidirect |
| 242. C47 | #10088 | semidirect |
| 256. C4⋊Q8 | C22⋊D47 | semidirect |
| 262. #127 | C22⋊D47 | semidirect |
| 279. C4⋊C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253841 | 2 |
| #20249496 | 2 |
| #20242101 | 2 |
| #20241986 | 2 |
| #20241896 | 2 |
| #20241280 | 2 |
| C47×#3213 | 2 |
| #10088 | 47 |