Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 9. #15689502 | C4 | semidirect |
| 10. #15689475 | C4 | semidirect |
| 91. C42×C47 | Q16 | semidirect |
| 192. C47 | #9297 | semidirect |
| 268. C42 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254333 | 2 |
| #20246136 | 2 |
| #20242070 | 2 |
| #20241952 | 2 |
| #20241248 | 2 |
| #20241217 | 2 |
| C47×#1995 | 2 |
| #9297 | 47 |