Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20241817 | C2 | semidirect |
| 5. #20241285 | C2 | semidirect |
| 6. #20241233 | C2 | semidirect |
| 7. C47×#1985 | C2 | semidirect |
| 97. C2×C8×C47 | SD16 | semidirect |
| 182. #1985 | D47 | semidirect |
| 214. C47 | #9047 | semidirect |
| 291. C2×C8 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253419 | 2 |
| #20252107 | 2 |
| #20242038 | 2 |
| #20241817 | 2 |
| #20241285 | 2 |
| #20241233 | 2 |
| C47×#1985 | 2 |
| #9047 | 47 |