Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20245644 | C2 | semidirect |
| 3. #20245643 | C2 | semidirect |
| 4. #20243004 | C2 | semidirect |
| 6. C16×C47⋊C8 | C2 | semidirect |
| 7. C47×#2248 | C2 | semidirect |
| 64. C16×C47 | D8 | semidirect |
| 65. C47⋊C16 | D8 | semidirect |
| 84. C47⋊C8 | SD32 | semidirect |
| 99. #2248 | D47 | semidirect |
| 120. C47 | #12517 | semidirect |
| 165. C16 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245645 | 2 |
| #20245644 | 2 |
| #20245643 | 2 |
| #20243004 | 2 |
| #20243002 | 2 |
| C16×C47⋊C8 | 2 |
| C47×#2248 | 2 |
| #12517 | 47 |