Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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×#15689564 | C2 | semidirect |
| 3. #20245322 | C2 | semidirect |
| 4. #20245305 | C2 | semidirect |
| 5. #20245108 | C2 | semidirect |
| 6. #20244999 | C2 | semidirect |
| 7. C23×Q16×C47 | C2 | semidirect |
| 11. C2×#13093970 | C22 | semidirect |
| 12. C2×#13093967 | C22 | semidirect |
| 19. #15688927 | C22 | semidirect |
| 61. C2×Q16×C47 | D4 | semidirect |
| 154. C22×C47 | #510 | semidirect |
| 165. C23×Q16 | D47 | semidirect |
| 197. C47 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D47 | semidirect |
| 325. C22 | #15689564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20252969 | 2 |
| #20245322 | 2 |
| #20245305 | 2 |
| #20245108 | 2 |
| #20244999 | 2 |
| C23×Q16×C47 | 2 |
| #33518 | 47 |