Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #20242073 | C2 | semidirect |
| 5. #20241246 | C2 | semidirect |
| 6. #20241219 | C2 | semidirect |
| 7. C47×#1993 | C2 | semidirect |
| 10. #15689497 | C4 | semidirect |
| 11. #15689473 | C4 | semidirect |
| 89. C2×C8×C47 | SD16 | semidirect |
| 171. #1993 | D47 | semidirect |
| 201. C47 | #9289 | semidirect |
| 272. C2×C8 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254313 | 2 |
| #20252107 | 2 |
| #20242073 | 2 |
| #20241947 | 2 |
| #20241246 | 2 |
| #20241219 | 2 |
| C47×#1993 | 2 |
| #9289 | 47 |