Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 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. C22×D752 | C2 | semidirect |
| 2. C2×#15689539 | C2 | semidirect |
| 3. #20253037 | C2 | semidirect |
| 4. #20245492 | C2 | semidirect |
| 5. #20245475 | C2 | semidirect |
| 6. #20245103 | C2 | semidirect |
| 7. C47×#2158 | C2 | semidirect |
| 16. C2×#13093963 | C22 | semidirect |
| 17. C2×C16×D47 | C22 | semidirect |
| 19. #15689360 | C22 | semidirect |
| 21. #15688923 | C22 | semidirect |
| 24. C47×#367 | C22 | semidirect |
| 25. C47×#366 | C22 | semidirect |
| 50. C2×C16×C47 | D4 | semidirect |
| 130. #2158 | D47 | semidirect |
| 152. #367 | C2×D47 | semidirect |
| 153. #366 | C2×D47 | semidirect |
| 155. C47 | #33607 | semidirect |
| 179. C2×C16 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D752 | 2 |
| C2×#15689539 | 2 |
| #20253037 | 2 |
| #20245492 | 2 |
| #20245475 | 2 |
| #20245103 | 2 |
| C47×#2158 | 2 |
| #33607 | 47 |