Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×C16×D47 | C2 | semidirect |
| 3. C2×#15688931 | C2 | semidirect |
| 4. C2×#15688929 | C2 | semidirect |
| 5. #20243423 | C2 | semidirect |
| 6. #20241483 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 51. C2×C47⋊C16 | D4 | semidirect |
| 63. C2×C16×C47 | D4 | semidirect |
| 167. C2×D47 | #359 | semidirect |
| 181. #1382 | D47 | semidirect |
| 207. C47 | #13063 | semidirect |
| 239. C2×C16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D47 | 2 |
| #20252970 | 2 |
| C2×#15688931 | 2 |
| C2×#15688929 | 2 |
| #20243423 | 2 |
| #20241483 | 2 |
| C47×#1382 | 2 |
| #13063 | 47 |