Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
960 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20244205 | C2 | semidirect |
| 2. C2×#15688863 | C2 | semidirect |
| 6. C2×#13093935 | C22 | semidirect |
| 7. #15688993 | C22 | semidirect |
| 10. C47×H(3,𝔽4) | C4 | semidirect |
| 108. H(3,𝔽4) | Dic47 | semidirect |
| 117. C47 | #8506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244205 | 2 |
| C2×#15688863 | 2 |
| C2×C47×H(3,𝔽4) | 2 |
| #8506 | 47 |