Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
726 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #20241317 | C2 | direct (N × H) |
| 27. C23×Dic47 | C8 | semidirect |
| 90. C22×Dic47 | C2×C8 | semidirect |
| 202. C2×C47 | #1317 | semidirect |
| 221. C47 | C2×#1317 | semidirect |
| 399. C2 | #20241317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688984 | 2 |
| C2×#15688847 | 2 |
| #20241317 | 2 |
| C2×C47×#323 | 2 |
| C2×#1317 | 47 |