Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20254695 | C2 | semidirect |
| 2. #20253480 | C2 | semidirect |
| 3. #20253475 | C2 | semidirect |
| 4. #20244186 | C2 | semidirect |
| 5. #20241998 | C2 | semidirect |
| 6. #20241257 | C2 | semidirect |
| 7. C47×#1530 | C2 | semidirect |
| 213. #1530 | D47 | semidirect |
| 247. C47 | #10026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254695 | 2 |
| #20253480 | 2 |
| #20253475 | 2 |
| #20244186 | 2 |
| #20241998 | 2 |
| #20241257 | 2 |
| C47×#1530 | 2 |
| #10026 | 47 |