Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 19. #15688938 | C4 | semidirect |
| 176. C47 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252257 | 2 |
| #20245174 | 2 |
| C2×#15688938 | 2 |
| C2×#15688926 | 2 |
| #20241485 | 2 |
| #20241477 | 2 |
| C47×#1952 | 2 |
| #12941 | 47 |