Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #20260691 | C2 | semidirect |
| 3. C4×#13095495 | C2 | semidirect |
| 4. C2×#15690721 | C2 | semidirect |
| 6. #15690817 | C4 | semidirect |
| 18. #13095495 | C2×C4 | semidirect |
| 19. C2×#11715895 | C2×C4 | semidirect |
| 54. C97 | #2875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| #20260691 | 2 |
| C4×#13095495 | 2 |
| C2×#15690721 | 2 |
| C4×#41×C97 | 2 |
| #2875 | 97 |