Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1060 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20254136 | C2 | semidirect |
| 2. C2×#15689256 | C2 | semidirect |
| 3. #20247025 | C2 | semidirect |
| 4. #20243318 | C2 | semidirect |
| 5. #20241955 | C2 | semidirect |
| 6. #20241236 | C2 | semidirect |
| 7. C47×#1964 | C2 | semidirect |
| 46. C22×C47⋊C8 | D4 | semidirect |
| 65. C22⋊(C47⋊C8) | D4 | semidirect |
| 67. C22×D4×C47 | D4 | semidirect |
| 74. C2×C4⋊C4×C47 | D4 | semidirect |
| 140. C22⋊C4×C47 | D8 | semidirect |
| 262. #1964 | D47 | semidirect |
| 299. C47 | #9946 | semidirect |
| 312. C22×D4 | D188 | semidirect |
| 332. C2×C4⋊C4 | D188 | semidirect |
| 420. C22⋊C4 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254136 | 2 |
| C2×#15689256 | 2 |
| #20247025 | 2 |
| #20243318 | 2 |
| #20241955 | 2 |
| #20241236 | 2 |
| C47×#1964 | 2 |
| #9946 | 47 |