Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1284 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#15689295 | C2 | semidirect |
| 2. #20245405 | C2 | direct (N × H) |
| 3. C2×#15688920 | C2 | semidirect |
| 4. C2×C47×H(3,𝔽4) | C2 | semidirect |
| 5. C2×#13094072 | C22 | semidirect |
| 8. #15689295 | C22 | semidirect |
| 10. C2×#13093943 | C22 | semidirect |
| 11. #15688920 | C22 | semidirect |
| 13. C47×H(3,𝔽4) | C22 | semidirect |
| 19. #13094072 | C23 | semidirect |
| 30. #13093943 | C23 | semidirect |
| 135. C2×H(3,𝔽4) | D47 | semidirect |
| 142. C2×C47 | #2202 | semidirect |
| 148. H(3,𝔽4) | C2×D47 | semidirect |
| 157. C47 | C2×#2202 | semidirect |
| 279. C2 | #20245405 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689295 | 2 |
| #20245405 | 2 |
| C2×#15688920 | 2 |
| C2×C47×H(3,𝔽4) | 2 |
| C2×#2202 | 47 |