Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
780 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#15689513 | C2 | semidirect |
| 2. C2×#15689512 | C2 | semidirect |
| 3. #20251433 | C2 | semidirect |
| 4. #20244212 | C2 | semidirect |
| 5. C2×#15688862 | C2 | semidirect |
| 6. #20241270 | C2 | semidirect |
| 7. C2×C47×#329 | C2 | semidirect |
| 49. #13094021 | D4 | semidirect |
| 61. #13093935 | D4 | semidirect |
| 79. #97×C47 | D4 | semidirect |
| 230. C2×#329 | D47 | semidirect |
| 263. C47 | #10078 | semidirect |
| 309. #97 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689513 | 2 |
| C2×#15689512 | 2 |
| #20251433 | 2 |
| #20244212 | 2 |
| C2×#15688862 | 2 |
| #20241270 | 2 |
| C2×C47×#329 | 2 |
| #10078 | 47 |