Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245428 | C2 | semidirect |
| 3. Q16×C47⋊C8 | C2 | semidirect |
| 4. #20241457 | C2 | semidirect |
| 5. #20241435 | C2 | semidirect |
| 6. #20241434 | C2 | semidirect |
| 7. C47×#2207 | C2 | semidirect |
| 54. Q16×C47 | D8 | semidirect |
| 101. C47⋊C8 | SD32 | semidirect |
| 118. #2207 | D47 | semidirect |
| 144. C47 | #12425 | semidirect |
| 176. Q16 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245428 | 2 |
| #20243002 | 2 |
| Q16×C47⋊C8 | 2 |
| #20241457 | 2 |
| #20241435 | 2 |
| #20241434 | 2 |
| C47×#2207 | 2 |
| #12425 | 47 |