Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20254371 | C2 | semidirect |
| 2. #20253841 | C2 | semidirect |
| 3. #20249494 | C2 | semidirect |
| 4. #20242101 | C2 | semidirect |
| 5. #20241987 | C2 | semidirect |
| 6. #20241281 | C2 | semidirect |
| 7. C47×#1505 | C2 | semidirect |
| 56. C4⋊(C47⋊C8) | D4 | semidirect |
| 61. #13093935 | D4 | semidirect |
| 64. C4⋊Q8×C47 | D4 | semidirect |
| 65. #127×C47 | D4 | semidirect |
| 210. #1505 | D47 | semidirect |
| 242. C47 | #10088 | semidirect |
| 256. C4⋊Q8 | D188 | semidirect |
| 262. #127 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254371 | 2 |
| #20253841 | 2 |
| #20249494 | 2 |
| #20242101 | 2 |
| #20241987 | 2 |
| #20241281 | 2 |
| C47×#1505 | 2 |
| #10088 | 47 |