Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15688945 | C2 | semidirect |
| 4. #20244124 | C2 | semidirect |
| 5. #20241497 | C2 | semidirect |
| 6. #20241467 | C2 | semidirect |
| 18. #15688927 | C4 | semidirect |
| 19. #15688924 | C4 | semidirect |
| 73. Q16×C47 | C4⋊C4 | semidirect |
| 77. D8×C47 | C4⋊C4 | semidirect |
| 180. C47 | #12955 | semidirect |
| 229. Q16 | Dic47⋊C4 | semidirect |
| 233. D8 | Dic47⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689245 | 2 |
| C2×#15688945 | 2 |
| #20245100 | 2 |
| #20244124 | 2 |
| #20241497 | 2 |
| #20241467 | 2 |
| C2×C47×#360 | 2 |
| #12955 | 47 |