Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20252048 | C2 | semidirect |
| 3. #20243485 | C2 | semidirect |
| 6. #20241235 | C2 | semidirect |
| 7. C47×#1293 | C2 | semidirect |
| 17. C2×#13093958 | C4 | semidirect |
| 18. C2×#13093956 | C4 | semidirect |
| 20. C2×#13093946 | C4 | semidirect |
| 21. C2×#13093946 | C4 | semidirect |
| 221. #1293 | D47 | semidirect |
| 256. C47 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689448 | 2 |
| #20252048 | 2 |
| #20243485 | 2 |
| #20241905 | 2 |
| #20241749 | 2 |
| #20241235 | 2 |
| C47×#1293 | 2 |
| #9242 | 47 |