Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
242 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20245221 | C2 | semidirect |
| 3. #20241457 | C2 | semidirect |
| 4. D4⋊(C47⋊C16) | C2 | semidirect |
| 5. #20241342 | C2 | semidirect |
| 6. C16×C47⋊C8 | C2 | semidirect |
| 7. C47×#2169 | C2 | semidirect |
| 68. C16×C47 | D8 | semidirect |
| 93. C47⋊C8 | M32 | semidirect |
| 110. #2169 | D47 | semidirect |
| 136. C47 | #12039 | semidirect |
| 184. C16 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245221 | 2 |
| C8×#10625334 | 2 |
| #20241457 | 2 |
| D4⋊(C47⋊C16) | 2 |
| #20241342 | 2 |
| C16×C47⋊C8 | 2 |
| C47×#2169 | 2 |
| #12039 | 47 |