Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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×#13093963 | C2 | semidirect |
| 2. C2×#15689356 | C2 | semidirect |
| 3. #20245488 | C2 | direct (N × H) |
| 4. C2×#15688951 | C2 | semidirect |
| 5. C2×#15688924 | C2 | semidirect |
| 6. C22×D16×C47 | C2 | semidirect |
| 10. C2×#13093963 | C22 | semidirect |
| 13. #15689356 | C22 | semidirect |
| 16. #15688951 | C22 | semidirect |
| 17. #15688924 | C22 | semidirect |
| 20. C2×D16×C47 | C22 | semidirect |
| 46. C2×C16×C47 | D4 | semidirect |
| 78. C16×C47 | C2×D4 | semidirect |
| 123. C22×D16 | D47 | semidirect |
| 130. C2×C47 | #2218 | semidirect |
| 138. C2×D16 | C2×D47 | semidirect |
| 149. C47 | C2×#2218 | semidirect |
| 171. C2×C16 | C22⋊D47 | semidirect |
| 207. C16 | C2×C22⋊D47 | semidirect |
| 252. C2 | #20245488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093963 | 2 |
| C2×#15689356 | 2 |
| #20245488 | 2 |
| C2×#15688951 | 2 |
| C2×#15688924 | 2 |
| C22×D16×C47 | 2 |
| C2×#2218 | 47 |