Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
702 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C22×#13093943 | C2 | semidirect |
| 2. C2×#15688920 | C2 | semidirect |
| 3. #20243312 | C2 | semidirect |
| 4. #20241515 | C2 | semidirect |
| 36. #13093943 | D4 | semidirect |
| 211. C22×C47 | #355 | semidirect |
| 257. C47 | #13092 | semidirect |
| 443. C22 | #15688920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093943 | 2 |
| C2×#15688920 | 2 |
| #20243312 | 2 |
| #20241515 | 2 |
| C47×#2436 | 2 |
| #13092 | 47 |