Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 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. #20254371 | C2 | semidirect |
| 2. #20248327 | C2 | semidirect |
| 3. #20244308 | C2 | semidirect |
| 4. #20241987 | C2 | semidirect |
| 5. #20241831 | C2 | semidirect |
| 6. #20241243 | C2 | semidirect |
| 7. C47×#3109 | C2 | semidirect |
| 52. C4⋊(C47⋊C8) | D4 | semidirect |
| 65. C4⋊Q8×C47 | D4 | semidirect |
| 66. #127×C47 | D4 | semidirect |
| 84. #97×C47 | D4 | semidirect |
| 232. #3109 | D47 | semidirect |
| 271. C47 | #10004 | semidirect |
| 282. C4⋊Q8 | C22⋊D47 | semidirect |
| 283. #127 | C22⋊D47 | semidirect |
| 321. #97 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254371 | 2 |
| #20248327 | 2 |
| #20244308 | 2 |
| #20241987 | 2 |
| #20241831 | 2 |
| #20241243 | 2 |
| C47×#3109 | 2 |
| #10004 | 47 |