Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
794 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20243857 | C2 | semidirect |
| 3. #20241752 | C2 | semidirect |
| 144. C23×C47 | #101 | semidirect |
| 174. C2×C4×C47 | #101 | semidirect |
| 239. C47 | #8537 | semidirect |
| 357. C23 | #13093943 | semidirect |
| 387. C2×C4 | #13093943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20243857 | 2 |
| #20243686 | 2 |
| #20241752 | 2 |
| #20241726 | 2 |
| C47×#3501 | 2 |
| #8537 | 47 |