Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20245624 | C2 | semidirect |
| 2. #20245535 | C2 | semidirect |
| 3. #20242901 | C2 | semidirect |
| 4. #20241431 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241346 | C2 | semidirect |
| 8. #15689528 | C22 | semidirect |
| 11. C4⋊(C47⋊C16) | C22 | semidirect |
| 15. #15688899 | C22 | semidirect |
| 16. #15688874 | C22 | semidirect |
| 85. D8×C47 | SD16 | semidirect |
| 193. C47 | #12378 | semidirect |
| 253. D8 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245624 | 2 |
| #20245535 | 2 |
| #20242901 | 2 |
| #20241431 | 2 |
| #20241355 | 2 |
| #20241346 | 2 |
| C47×#3273 | 2 |
| #12378 | 47 |