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×#15688847 | C2 | semidirect |
| 3. #20241384 | C2 | direct (N × H) |
| 4. C2×C47×#342 | C2 | semidirect |
| 5. C23×D188 | C4 | semidirect |
| 11. #15689032 | C4 | semidirect |
| 13. C2×C47⋊#95 | C4 | semidirect |
| 15. #15688847 | C22 | semidirect |
| 19. C47×#342 | C22 | semidirect |
| 25. C22×D188 | C2×C4 | semidirect |
| 40. C47⋊#95 | C2×C4 | semidirect |
| 238. C2×#342 | D47 | semidirect |
| 247. C2×C47 | #1343 | semidirect |
| 264. #342 | C2×D47 | semidirect |
| 267. C47 | C2×#1343 | semidirect |
| 491. C2 | #20241384 | 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×#15688847 | 2 |
| #20241384 | 2 |
| C2×C47×#342 | 2 |
| C2×#1343 | 47 |