Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#13093965 | C2 | semidirect |
| 2. C2×#15689394 | C2 | semidirect |
| 3. #20253032 | C2 | semidirect |
| 4. #20245105 | C2 | semidirect |
| 5. C2×#15688908 | C2 | semidirect |
| 6. #20241485 | C2 | semidirect |
| 7. C2×C47×#361 | C2 | semidirect |
| 40. C2×D376 | D4 | semidirect |
| 56. C2×C47⋊C16 | D4 | semidirect |
| 74. #108×C47 | D4 | semidirect |
| 196. C2×#361 | D47 | semidirect |
| 228. C47 | #13319 | semidirect |
| 270. #108 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093965 | 2 |
| C2×#15689394 | 2 |
| #20253032 | 2 |
| #20245105 | 2 |
| C2×#15688908 | 2 |
| #20241485 | 2 |
| C2×C47×#361 | 2 |
| #13319 | 47 |