Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1092 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#15689873 | C2 | semidirect |
| 2. C2×#15689306 | C2 | semidirect |
| 3. #20245408 | C2 | direct (N × H) |
| 4. C2×#15688921 | C2 | semidirect |
| 5. C2×#15688920 | C2 | semidirect |
| 10. #15689873 | C22 | semidirect |
| 17. #15689306 | C22 | semidirect |
| 20. #15688921 | C22 | semidirect |
| 21. #15688920 | C22 | semidirect |
| 225. C2×C47 | #2203 | semidirect |
| 249. C47 | C2×#2203 | semidirect |
| 439. C2 | #20245408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689873 | 2 |
| C2×#15689306 | 2 |
| #20245408 | 2 |
| C2×#15688921 | 2 |
| C2×#15688920 | 2 |
| C2×C47×#454 | 2 |
| C2×#2203 | 47 |