Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#15689390 | C2 | semidirect |
| 2. #20253054 | C2 | semidirect |
| 3. C2×#15688930 | C2 | semidirect |
| 4. C2×#15688924 | C2 | semidirect |
| 5. C2×#15688908 | C2 | semidirect |
| 6. #20241497 | C2 | semidirect |
| 7. C2×C47×#509 | C2 | semidirect |
| 54. #13093960 | D4 | semidirect |
| 74. C2×D8×C47 | D4 | semidirect |
| 79. M32×C47 | D4 | semidirect |
| 211. C2×#509 | D47 | semidirect |
| 249. C47 | #13307 | semidirect |
| 269. C2×D8 | C22⋊D47 | semidirect |
| 288. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689390 | 2 |
| #20253054 | 2 |
| C2×#15688930 | 2 |
| C2×#15688924 | 2 |
| C2×#15688908 | 2 |
| #20241497 | 2 |
| C2×C47×#509 | 2 |
| #13307 | 47 |