Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1164 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#15688890 | C2 | semidirect |
| 3. #20241386 | C2 | direct (N × H) |
| 4. C2×C47×#323 | C2 | semidirect |
| 5. C23×D188 | C4 | semidirect |
| 11. #15689032 | C4 | semidirect |
| 13. C2×C47⋊#95 | C4 | semidirect |
| 15. #15688890 | C22 | semidirect |
| 19. C47×#323 | C22 | semidirect |
| 25. C22×D188 | C2×C4 | semidirect |
| 42. C47⋊#95 | C2×C4 | semidirect |
| 239. C2×#323 | D47 | semidirect |
| 247. C2×C47 | #1343 | semidirect |
| 266. #323 | C2×D47 | semidirect |
| 267. C47 | C2×#1343 | semidirect |
| 491. C2 | #20241386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689032 | 2 |
| C2×#15688890 | 2 |
| #20241386 | 2 |
| C2×C47×#323 | 2 |
| C2×#1343 | 47 |