Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #20242272 | C2 | semidirect |
| 3. #20241348 | C2 | semidirect |
| 4. #20241304 | C2 | semidirect |
| 5. C47×#1372 | C2 | semidirect |
| 44. C16×C47 | M16 | semidirect |
| 73. #1372 | D47 | semidirect |
| 90. C47 | #12086 | semidirect |
| 120. C16 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D752 | 2 |
| #20242272 | 2 |
| #20241348 | 2 |
| #20241304 | 2 |
| C47×#1372 | 2 |
| #12086 | 47 |