Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
616 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 153 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. #97×Dic47 | C2 | semidirect |
| 4. #20241270 | C2 | semidirect |
| 17. #15688863 | C4 | semidirect |
| 20. C47×#329 | C4 | semidirect |
| 36. #13093935 | C2×C4 | semidirect |
| 50. #97×C47 | C2×C4 | semidirect |
| 146. Dic47 | #329 | direct (N × H) |
| 172. #329 | Dic47 | direct (N × H) |
| 173. C47 | C4×#329 | semidirect |
| 200. #97 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×Dic47 | 2 |
| #97×Dic47 | 2 |
| C2×#15688863 | 2 |
| #20241270 | 2 |
| C2×C47×#329 | 2 |
| C4×#329 | 47 |