Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15689558 | C2 | semidirect |
| 2. #20253104 | C2 | semidirect |
| 3. #20253037 | C2 | semidirect |
| 4. C2×#15688937 | C2 | semidirect |
| 5. #20245015 | C2 | semidirect |
| 6. #20241504 | C2 | semidirect |
| 7. C47×#2145 | C2 | semidirect |
| 59. #13093964 | D4 | semidirect |
| 62. #13093960 | D4 | semidirect |
| 71. C2×Q16×C47 | D4 | semidirect |
| 73. C2×D8×C47 | D4 | semidirect |
| 209. #2145 | D47 | semidirect |
| 242. C47 | #13310 | semidirect |
| 255. C2×Q16 | D188 | semidirect |
| 263. C2×D8 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| #20253104 | 2 |
| #20253037 | 2 |
| C2×#15688937 | 2 |
| #20245015 | 2 |
| #20241504 | 2 |
| C47×#2145 | 2 |
| #13310 | 47 |