Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2286 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 555 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. C2×#15688991 | C2 | semidirect |
| 2. #20241615 | C2 | semidirect |
| 11. C22×C42×C47 | C4 | semidirect |
| 51. C42×C47 | C22⋊C4 | semidirect |
| 79. C22×C47 | #383 | semidirect |
| 101. C22×C42 | Dic47 | semidirect |
| 107. C47 | #14683 | semidirect |
| 146. C42 | C22⋊Dic47 | semidirect |
| 172. C22 | #15688991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688991 | 2 |
| #20241615 | 2 |
| #20241611 | 2 |
| C23×C42×C47 | 2 |
| #14683 | 47 |