Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20245290 | C2 | semidirect |
| 4. #20241366 | C2 | semidirect |
| 6. C8×C47⋊C16 | C2 | semidirect |
| 7. C47×#1367 | C2 | semidirect |
| 60. #10625325 | C16 | semidirect |
| 67. C47⋊C16 | SD16 | semidirect |
| 80. Dic94 | C2×C16 | semidirect |
| 84. C8×C47 | C2×C16 | semidirect |
| 105. #1367 | D47 | semidirect |
| 128. C47 | C16×SD16 | semidirect |
| 192. C8 | C16×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245290 | 2 |
| #20245207 | 2 |
| C8×#10625325 | 2 |
| #20241366 | 2 |
| #20241342 | 2 |
| C8×C47⋊C16 | 2 |
| C47×#1367 | 2 |
| C16×SD16 | 47 |