Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20241691 | C2 | semidirect |
| 3. #20241363 | C2 | semidirect |
| 4. #20241360 | C2 | semidirect |
| 5. C47×#2165 | C2 | semidirect |
| 16. #15688844 | C22 | semidirect |
| 17. C8×C47⋊C8 | C22 | semidirect |
| 19. C47×#364 | C22 | semidirect |
| 74. Dic188 | M16 | semidirect |
| 76. D376 | M16 | semidirect |
| 122. #2165 | D47 | semidirect |
| 140. #364 | C2×D47 | semidirect |
| 146. C47 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252299 | 2 |
| #20241691 | 2 |
| #20241363 | 2 |
| #20241360 | 2 |
| C47×#2165 | 2 |
| #11669 | 47 |