Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1150 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 187 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×#15689518 | C2 | semidirect |
| 2. C2×#15689482 | C2 | semidirect |
| 3. #20242694 | C2 | direct (N × H) |
| 4. C2×#15688863 | C2 | semidirect |
| 5. C2×#15688863 | C2 | semidirect |
| 9. C2×#13094024 | C22 | semidirect |
| 11. #15689518 | C22 | semidirect |
| 13. #15689482 | C22 | semidirect |
| 16. C2×#13093935 | C22 | semidirect |
| 17. C2×#13093935 | C22 | semidirect |
| 18. #15688863 | C22 | semidirect |
| 19. #15688863 | C22 | semidirect |
| 38. #13094024 | C23 | semidirect |
| 44. #13093935 | C23 | semidirect |
| 45. #13093935 | C23 | semidirect |
| 190. C2×C47 | #1659 | semidirect |
| 215. C47 | C2×#1659 | semidirect |
| 370. C2 | #20242694 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689518 | 2 |
| C2×#15689482 | 2 |
| #20242694 | 2 |
| C2×#15688863 | 2 |
| C2×C47×H(3,𝔽4) | 2 |
| C2×#1659 | 47 |