Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 68. C2×Q8×C47 | Q16 | semidirect |
| 95. C4⋊C4×C47 | Q16 | semidirect |
| 211. C47 | #7784 | semidirect |
| 259. C2×Q8 | #10625337 | semidirect |
| 294. C4⋊C4 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244716 | 2 |
| #20244529 | 2 |
| #20244487 | 2 |
| #20241214 | 2 |
| #20241211 | 2 |
| C47×#2806 | 2 |
| #7784 | 47 |