Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 12. #15688845 | C4 | semidirect |
| 13. #15688845 | C4 | semidirect |
| 14. #15688844 | C4 | semidirect |
| 15. C8×C47⋊C8 | C4 | semidirect |
| 120. C47 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20241691 | 2 |
| #20241261 | 2 |
| #20241259 | 2 |
| #20241254 | 2 |
| #20241253 | 2 |
| C47×#1291 | 2 |
| #8803 | 47 |