Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#15689170 | C2 | semidirect |
| 3. #20245117 | C2 | semidirect |
| 4. #20245115 | C2 | semidirect |
| 5. C2×#15688904 | C2 | semidirect |
| 6. #20241504 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 57. #13093960 | D4 | semidirect |
| 68. #108×C47 | D4 | semidirect |
| 185. #1389 | D47 | semidirect |
| 211. C47 | #12998 | semidirect |
| 251. #108 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252998 | 2 |
| C2×#15689170 | 2 |
| #20245117 | 2 |
| #20245115 | 2 |
| C2×#15688904 | 2 |
| #20241504 | 2 |
| C47×#1389 | 2 |
| #12998 | 47 |