Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #20242158 | C2 | semidirect |
| 4. #20241952 | C2 | semidirect |
| 6. #20241247 | C2 | semidirect |
| 7. C47×#1542 | C2 | semidirect |
| 170. #1542 | D47 | semidirect |
| 199. C47 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253181 | 2 |
| #20243399 | 2 |
| #20242158 | 2 |
| #20241952 | 2 |
| #20241708 | 2 |
| #20241247 | 2 |
| C47×#1542 | 2 |
| #10468 | 47 |