Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
934 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20244193 | C2 | semidirect |
| 4. C47⋊#1273 | C2 | semidirect |
| 5. C47×#1957 | C2 | semidirect |
| 73. C2×C8×C47 | D8 | semidirect |
| 82. C2×C47⋊C8 | D8 | semidirect |
| 145. #1957 | D47 | semidirect |
| 166. C47 | #10304 | semidirect |
| 227. C2×C8 | #10625334 | semidirect |
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 |
| #20244193 | 2 |
| C47⋊#1273 | 2 |
| C47×#1957 | 2 |
| #10304 | 47 |