Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. #20241998 | C2 | semidirect |
| 3. #20241822 | C2 | semidirect |
| 4. #20241806 | C2 | semidirect |
| 5. #20241287 | C2 | semidirect |
| 6. #20241260 | C2 | semidirect |
| 7. C47×#2923 | C2 | semidirect |
| 185. #2923 | D47 | semidirect |
| 220. C47 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253539 | 2 |
| #20241998 | 2 |
| #20241822 | 2 |
| #20241806 | 2 |
| #20241287 | 2 |
| #20241260 | 2 |
| C47×#2923 | 2 |
| #9313 | 47 |