Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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×D752 | C2 | semidirect |
| 2. C2×#15688958 | C2 | semidirect |
| 3. #20241565 | C2 | semidirect |
| 4. C22⋊(C47⋊C32) | C2 | semidirect |
| 5. C47×#2215 | C2 | semidirect |
| 11. C2×C47⋊C32 | C22 | semidirect |
| 12. C2×D16×C47 | C22 | semidirect |
| 15. C47×#366 | C22 | semidirect |
| 24. D752 | D4 | semidirect |
| 82. C22×C47 | D32 | semidirect |
| 94. #2215 | D47 | semidirect |
| 107. C2×D16 | C2×D47 | semidirect |
| 112. #366 | C2×D47 | semidirect |
| 114. C47 | #13661 | semidirect |
| 183. C22 | #15688958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D752 | 2 |
| C2×#15688958 | 2 |
| #20241565 | 2 |
| C22⋊(C47⋊C32) | 2 |
| C47×#2215 | 2 |
| #13661 | 47 |