Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
226 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 226 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. #20242284 | C2 | semidirect |
| 4. #20241459 | C2 | semidirect |
| 5. #20241353 | C2 | semidirect |
| 6. #20241307 | C2 | semidirect |
| 128. C47 | #12074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093968 | 2 |
| #20242284 | 2 |
| D8×C47⋊C8 | 2 |
| #20241459 | 2 |
| #20241353 | 2 |
| #20241307 | 2 |
| C47×#1331 | 2 |
| #12074 | 47 |