Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 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. #20245645 | C2 | semidirect |
| 2. #20245423 | C2 | semidirect |
| 3. #20242743 | C2 | semidirect |
| 4. #20241437 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. C47×#3283 | C2 | semidirect |
| 73. D8×C47 | D8 | semidirect |
| 145. #3283 | D47 | semidirect |
| 175. C47 | #12319 | semidirect |
| 228. D8 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245645 | 2 |
| #20245423 | 2 |
| #20242743 | 2 |
| #20241437 | 2 |
| #20241349 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#3283 | 2 |
| #12319 | 47 |