Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #20261660 | C2 | direct (N × H) |
| 12. #15690749 | C4 | semidirect |
| 14. C2×#13095486 | C4 | semidirect |
| 15. C2×C16×C97 | C4 | semidirect |
| 28. #13095486 | C2×C4 | semidirect |
| 30. C16×C97 | C2×C4 | semidirect |
| 54. C2×C97 | #365 | semidirect |
| 59. C97 | C2×#365 | semidirect |
| 70. C2×C16 | #87604 | semidirect |
| 89. C16 | C2×#87604 | semidirect |
| 115. C2 | #20261660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690880 | 2 |
| C2×#15690878 | 2 |
| #20261660 | 2 |
| C2×#15690749 | 2 |
| C2×#365 | 97 |