Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1502 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#15688917 | C2 | direct (N × H) |
| 5. C23×Dic94 | C4 | semidirect |
| 8. C2×#13094011 | C4 | semidirect |
| 13. C22×C4×Dic47 | C4 | semidirect |
| 16. #15688917 | C22 | direct (N × H) |
| 24. C22×Dic94 | C2×C4 | semidirect |
| 31. #13094011 | C2×C4 | semidirect |
| 40. C2×C4×Dic47 | C2×C4 | semidirect |
| 99. C2×Dic94 | C22×C4 | semidirect |
| 109. C4×Dic47 | C22×C4 | semidirect |
| 175. C22×C47 | #354 | semidirect |
| 195. C2×C47 | C2×#354 | semidirect |
| 213. C47 | C22×#354 | semidirect |
| 367. C22 | #15688917 | direct (N × H) |
| 383. C2 | C2×#15688917 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094011 | 2 |
| C22×#13093939 | 2 |
| C2×#15688917 | 2 |
| C22×#99×C47 | 2 |
| C22×#354 | 47 |