Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20242116 | C2 | semidirect |
| 4. #20242002 | C2 | semidirect |
| 6. #20241299 | C2 | semidirect |
| 7. C47×#1838 | C2 | semidirect |
| 150. #1838 | D47 | semidirect |
| 180. C47 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254776 | 2 |
| #20242116 | 2 |
| #20242108 | 2 |
| #20242002 | 2 |
| #20241998 | 2 |
| #20241299 | 2 |
| C47×#1838 | 2 |
| #10527 | 47 |