Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20254308 | C2 | semidirect |
| 2. #20254303 | C2 | semidirect |
| 3. #20253833 | C2 | semidirect |
| 4. #20244211 | C2 | semidirect |
| 5. #20241947 | C2 | semidirect |
| 6. #20241232 | C2 | semidirect |
| 7. C47×#1517 | C2 | semidirect |
| 131. C2×C47⋊C8 | D8 | semidirect |
| 210. #1517 | D47 | semidirect |
| 243. C47 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254308 | 2 |
| #20254303 | 2 |
| #20253833 | 2 |
| #20244211 | 2 |
| #20241947 | 2 |
| #20241232 | 2 |
| C47×#1517 | 2 |
| #10218 | 47 |