Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#15689240 | C2 | semidirect |
| 3. C2×#15688937 | C2 | semidirect |
| 4. #20244252 | C2 | semidirect |
| 5. #20241496 | C2 | semidirect |
| 6. #20241469 | C2 | semidirect |
| 7. C47×#2139 | C2 | semidirect |
| 11. #15689558 | C4 | semidirect |
| 89. Q16×C47 | C22⋊C4 | semidirect |
| 93. D8×C47 | C22⋊C4 | semidirect |
| 182. #2139 | D47 | semidirect |
| 213. C47 | #13029 | semidirect |
| 275. Q16 | (C2×D47)⋊C4 | semidirect |
| 283. D8 | (C2×D47)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| C2×#15689240 | 2 |
| C2×#15688937 | 2 |
| #20244252 | 2 |
| #20241496 | 2 |
| #20241469 | 2 |
| C47×#2139 | 2 |
| #13029 | 47 |