Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#15689554 | C2 | semidirect |
| 2. #20253817 | C2 | semidirect |
| 3. #20253815 | C2 | semidirect |
| 4. #20245648 | C2 | semidirect |
| 5. #20245644 | C2 | semidirect |
| 6. #20245640 | C2 | semidirect |
| 7. #20245637 | C2 | semidirect |
| 8. C4×C16×D47 | C2 | semidirect |
| 9. C47×#2248 | C2 | semidirect |
| 65. C16×D47 | D4 | semidirect |
| 160. C4×C47 | #508 | semidirect |
| 171. #2248 | D47 | semidirect |
| 206. C47 | #33713 | semidirect |
| 333. C4 | #15689554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689554 | 2 |
| #20253817 | 2 |
| #20253815 | 2 |
| #20245648 | 2 |
| #20245644 | 2 |
| #20245640 | 2 |
| #20245637 | 2 |
| C4×C16×D47 | 2 |
| C47×#2248 | 2 |
| #33713 | 47 |