Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 79 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×#15688920 | C2 | semidirect |
| 2. C2×#15688918 | C2 | semidirect |
| 3. #20241548 | C2 | semidirect |
| 4. #20241545 | C2 | semidirect |
| 14. C47×#532 | C4 | semidirect |
| 16. C47×#497 | C4 | semidirect |
| 18. C47×#496 | C4 | semidirect |
| 22. C4×M16×C47 | C4 | semidirect |
| 45. C4⋊Q8×C47 | C2×C4 | semidirect |
| 46. #127×C47 | C2×C4 | semidirect |
| 57. #97×C47 | C2×C4 | semidirect |
| 58. #97×C47 | C2×C4 | semidirect |
| 184. #532 | Dic47 | semidirect |
| 186. #497 | Dic47 | semidirect |
| 188. #496 | Dic47 | semidirect |
| 194. C4×M16 | Dic47 | semidirect |
| 199. C47 | #13578 | semidirect |
| 217. C4⋊Q8 | C2×Dic47 | semidirect |
| 218. #127 | C2×Dic47 | semidirect |
| 234. #97 | C2×Dic47 | semidirect |
| 235. #97 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688920 | 2 |
| C2×#15688918 | 2 |
| #20241548 | 2 |
| #20241545 | 2 |
| C47×#3153 | 2 |
| #13578 | 47 |