Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#15689518 | C2 | semidirect |
| 3. C2×#15689483 | C2 | semidirect |
| 4. #20242695 | C2 | direct (N × H) |
| 5. C2×#15688862 | C2 | semidirect |
| 6. C2×C47×#329 | C2 | semidirect |
| 12. C2×#13094024 | C22 | semidirect |
| 19. #15689518 | C22 | semidirect |
| 21. #15689483 | C22 | semidirect |
| 24. C2×#13093935 | C22 | semidirect |
| 25. #15688862 | C22 | semidirect |
| 27. C2×#97×C47 | C22 | semidirect |
| 28. C47×#329 | C22 | semidirect |
| 42. #13094024 | C23 | semidirect |
| 64. #13093935 | C23 | semidirect |
| 74. #97×C47 | C23 | semidirect |
| 187. C2×#329 | D47 | semidirect |
| 189. C2×C47 | #1659 | semidirect |
| 212. C2×#97 | C2×D47 | semidirect |
| 214. #329 | C2×D47 | semidirect |
| 215. C47 | C2×#1659 | semidirect |
| 261. #97 | C22×D47 | semidirect |
| 370. C2 | #20242695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689865 | 2 |
| C2×#15689518 | 2 |
| C2×#15689483 | 2 |
| #20242695 | 2 |
| C2×#15688862 | 2 |
| C2×C47×#329 | 2 |
| C2×#1659 | 47 |