Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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. #20245259 | C2 | direct (N × H) |
| 18. C2×Q32×C47 | C4 | semidirect |
| 41. Q32×C47 | C2×C4 | semidirect |
| 103. C2×C47 | #2176 | semidirect |
| 108. C2×Q32 | Dic47 | semidirect |
| 120. C47 | C2×#2176 | semidirect |
| 134. Q32 | C2×Dic47 | semidirect |
| 196. C2 | #20245259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×Dic47 | 2 |
| #20245259 | 2 |
| C2×#15688951 | 2 |
| C2×#15688927 | 2 |
| C2×#15688898 | 2 |
| C22×Q32×C47 | 2 |
| C2×#2176 | 47 |