Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#15689561 | C2 | semidirect |
| 2. #20253109 | C2 | semidirect |
| 3. #20253037 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20245123 | C2 | semidirect |
| 6. #20245017 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 43. C2×Dic188 | D4 | semidirect |
| 51. C2×D376 | D4 | semidirect |
| 75. M32×C47 | D4 | semidirect |
| 78. #108×C47 | D4 | semidirect |
| 211. #1389 | D47 | semidirect |
| 242. C47 | #13310 | semidirect |
| 283. M32 | D188 | semidirect |
| 287. #108 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689561 | 2 |
| #20253109 | 2 |
| #20253037 | 2 |
| C2×#15688935 | 2 |
| #20245123 | 2 |
| #20245017 | 2 |
| C47×#1389 | 2 |
| #13310 | 47 |