Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20245153 | C2 | semidirect |
| 4. C2×#15688901 | C2 | semidirect |
| 6. #20241473 | C2 | semidirect |
| 7. C47×#1377 | C2 | semidirect |
| 140. #1377 | D47 | semidirect |
| 161. C47 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245153 | 2 |
| #20245015 | 2 |
| #20245008 | 2 |
| C2×#15688901 | 2 |
| #20243232 | 2 |
| #20241473 | 2 |
| C47×#1377 | 2 |
| #13127 | 47 |