Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
802 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 2. C47⋊#1273 | C2 | semidirect |
| 3. C47×#1273 | C2 | semidirect |
| 32. C2×C8×C47 | M16 | semidirect |
| 39. C2×C47⋊C8 | M16 | semidirect |
| 68. #1273 | D47 | semidirect |
| 79. C47 | #7852 | semidirect |
| 106. C2×C8 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#10625324 | 2 |
| C47⋊#1273 | 2 |
| C47×#1273 | 2 |
| #7852 | 47 |