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. #20254375 | C2 | semidirect |
| 2. #20253479 | C2 | semidirect |
| 3. #20244306 | C2 | semidirect |
| 4. #20241986 | C2 | semidirect |
| 5. #20241831 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#2540 | C2 | semidirect |
| 38. #13094024 | D4 | semidirect |
| 39. #13094021 | D4 | semidirect |
| 47. C4⋊(C47⋊C8) | D4 | semidirect |
| 57. #13093935 | D4 | semidirect |
| 233. #2540 | D47 | semidirect |
| 271. C47 | #10004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254375 | 2 |
| #20253479 | 2 |
| #20244306 | 2 |
| #20241986 | 2 |
| #20241831 | 2 |
| #20241244 | 2 |
| C47×#2540 | 2 |
| #10004 | 47 |