Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20243376 | C2 | semidirect |
| 2. #20241709 | C2 | semidirect |
| 3. #20241385 | C2 | semidirect |
| 8. #15688890 | C22 | semidirect |
| 10. #15688847 | C22 | semidirect |
| 11. C23×D4×C47 | C4 | semidirect |
| 15. C47×#394 | C4 | semidirect |
| 18. C47×#380 | C4 | semidirect |
| 206. C23×D4 | Dic47 | semidirect |
| 212. #394 | Dic47 | semidirect |
| 216. #380 | Dic47 | semidirect |
| 221. C47 | #11873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20243376 | 2 |
| #20241709 | 2 |
| #20241385 | 2 |
| C47×#2408 | 2 |
| #11873 | 47 |