Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2062 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2062 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 |
|---|---|---|
| 2. C22×#13093939 | C2 | semidirect |
| 3. C2×#15688915 | C2 | direct (N × H) |
| 4. C22×#99×C47 | C2 | semidirect |
| 5. C23×D188 | C4 | semidirect |
| 10. C2×#13094020 | C4 | semidirect |
| 13. C22×C4×Dic47 | C4 | semidirect |
| 15. C2×#13093939 | C22 | semidirect |
| 16. #15688915 | C22 | direct (N × H) |
| 20. C2×#99×C47 | C22 | semidirect |
| 25. C22×D188 | C2×C4 | semidirect |
| 37. #13094020 | C2×C4 | semidirect |
| 42. C2×C4×Dic47 | C2×C4 | semidirect |
| 44. #13093939 | C23 | semidirect |
| 58. #99×C47 | C23 | semidirect |
| 111. C2×D188 | C22×C4 | semidirect |
| 117. C4×Dic47 | C22×C4 | semidirect |
| 191. C22×C47 | #353 | semidirect |
| 207. C22×#99 | D47 | semidirect |
| 215. C2×C47 | C2×#353 | semidirect |
| 232. C2×#99 | C2×D47 | semidirect |
| 234. C47 | C22×#353 | semidirect |
| 272. #99 | C22×D47 | semidirect |
| 409. C22 | #15688915 | direct (N × H) |
| 425. C2 | C2×#15688915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094020 | 2 |
| C22×#13093939 | 2 |
| C2×#15688915 | 2 |
| C22×#99×C47 | 2 |
| C22×#353 | 47 |