Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
202 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 89 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×#15688956 | C2 | semidirect |
| 3. Dic47⋊C32 | C2 | semidirect |
| 4. C22⋊(C47⋊C32) | C2 | semidirect |
| 5. (C2×D47)⋊C32 | C2 | semidirect |
| 6. C32×Dic47 | C2 | semidirect |
| 7. C2×C47×M64 | C2 | semidirect |
| 39. C32×C47 | D4 | semidirect |
| 90. Dic47 | M64 | semidirect |
| 92. C2×M64 | D47 | semidirect |
| 116. C47 | #13646 | semidirect |
| 135. C32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688956 | 2 |
| C16×C22⋊D47 | 2 |
| Dic47⋊C32 | 2 |
| C22⋊(C47⋊C32) | 2 |
| (C2×D47)⋊C32 | 2 |
| C32×Dic47 | 2 |
| C2×C47×M64 | 2 |
| #13646 | 47 |