Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
994 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 994 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×#15689519 | C2 | semidirect |
| 4. #20242976 | C2 | direct (N × H) |
| 5. C2×C8×C47⋊C8 | C2 | semidirect |
| 6. C2×C47×#498 | C2 | semidirect |
| 12. #15689519 | C22 | semidirect |
| 19. C8×C47⋊C8 | C22 | semidirect |
| 22. C47×#498 | C22 | semidirect |
| 72. C2×C8×C47 | SD16 | semidirect |
| 84. C2×C47⋊C8 | SD16 | semidirect |
| 109. C8×C47 | C2×SD16 | semidirect |
| 110. C47⋊C8 | C2×SD16 | semidirect |
| 125. C2×#498 | D47 | semidirect |
| 130. C2×C47 | #1705 | semidirect |
| 142. #498 | C2×D47 | semidirect |
| 152. C47 | C2×#1705 | semidirect |
| 204. C2×C8 | #10625336 | semidirect |
| 238. C8 | C2×#10625336 | semidirect |
| 252. C2 | #20242976 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689519 | 2 |
| C2×#15689497 | 2 |
| C2×#15689496 | 2 |
| #20242976 | 2 |
| C2×C8×C47⋊C8 | 2 |
| C2×C47×#498 | 2 |
| C2×#1705 | 47 |