Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #20246564 | C2 | direct (N × H) |
| 3. C2×#15689001 | C2 | semidirect |
| 4. C2×#15688991 | C2 | semidirect |
| 5. C2×C47×#383 | C2 | semidirect |
| 8. C2×#13094021 | C4 | semidirect |
| 11. #15689001 | C22 | semidirect |
| 12. #15688991 | C22 | semidirect |
| 15. C47×#383 | C22 | semidirect |
| 20. C22×D188 | C2×C4 | semidirect |
| 25. #13094021 | C2×C4 | semidirect |
| 31. C2×C42×C47 | C2×C4 | semidirect |
| 49. C2×D188 | C22×C4 | semidirect |
| 52. C42×C47 | C22×C4 | semidirect |
| 88. C2×#383 | D47 | semidirect |
| 89. C2×C47 | #2380 | semidirect |
| 101. #383 | C2×D47 | semidirect |
| 104. C47 | C2×#2380 | semidirect |
| 118. C2×C42 | C4×D47 | semidirect |
| 141. C42 | C2×C4×D47 | semidirect |
| 172. C2 | #20246564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094021 | 2 |
| #20246564 | 2 |
| C2×#15689001 | 2 |
| C2×#15688991 | 2 |
| C2×C47×#383 | 2 |
| C2×#2380 | 47 |