Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
534 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 147 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×C22⋊(C47⋊C16) | C2 | semidirect |
| 2. #20241314 | C2 | direct (N × H) |
| 6. C22⋊(C47⋊C16) | C22 | semidirect |
| 138. C2×C47 | #1315 | semidirect |
| 151. C47 | C2×#1315 | semidirect |
| 272. C2 | #20241314 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C47⋊C16) | 2 |
| #20241314 | 2 |
| C2×C47×#408 | 2 |
| C2×#1315 | 47 |