Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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×#15689500 | C2 | semidirect |
| 2. C2×#15689499 | C2 | semidirect |
| 3. #20243002 | C2 | direct (N × H) |
| 4. C2×C8×C47⋊C8 | C2 | semidirect |
| 5. C2×C47×#493 | C2 | semidirect |
| 10. #15689500 | C22 | semidirect |
| 12. #15689499 | C22 | semidirect |
| 14. C8×C47⋊C8 | C22 | semidirect |
| 18. C47×#493 | C22 | semidirect |
| 60. C2×C8×C47 | D8 | semidirect |
| 66. C2×C47⋊C8 | D8 | semidirect |
| 90. C8×C47 | C2×D8 | semidirect |
| 91. C47⋊C8 | C2×D8 | semidirect |
| 108. C2×#493 | D47 | semidirect |
| 112. C2×C47 | #1712 | semidirect |
| 126. #493 | C2×D47 | semidirect |
| 130. C47 | C2×#1712 | semidirect |
| 175. C2×C8 | #10625334 | semidirect |
| 202. C8 | C2×#10625334 | semidirect |
| 218. C2 | #20243002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689500 | 2 |
| C2×#15689499 | 2 |
| #20243002 | 2 |
| C2×C8×C47⋊C8 | 2 |
| C2×C47×#493 | 2 |
| C2×#1712 | 47 |