Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
366 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245611 | C2 | semidirect |
| 2. #20245530 | C2 | semidirect |
| 3. #20242777 | C2 | semidirect |
| 4. #20241434 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 67. Q16×C47 | SD16 | semidirect |
| 166. C47 | #12369 | semidirect |
| 209. Q16 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245611 | 2 |
| #20245530 | 2 |
| #20242777 | 2 |
| #20241434 | 2 |
| #20241352 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#3287 | 2 |
| #12369 | 47 |