Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C22⋊(C47⋊C16) | C2 | semidirect |
| 3. #20241402 | C2 | semidirect |
| 4. C47×#1810 | C2 | semidirect |
| 15. C22⋊(C47⋊C16) | C22 | semidirect |
| 19. C47×#341 | C22 | semidirect |
| 146. #1810 | D47 | semidirect |
| 169. #341 | C2×D47 | semidirect |
| 170. C47 | #11891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689359 | 2 |
| C2×C22⋊(C47⋊C16) | 2 |
| #20241402 | 2 |
| C47×#1810 | 2 |
| #11891 | 47 |