Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20261642 | C2 | direct (N × H) |
| 7. C22×Dic194 | C4 | semidirect |
| 10. #15690798 | C4 | semidirect |
| 13. C2×C42×C97 | C4 | semidirect |
| 21. C2×Dic194 | C2×C4 | semidirect |
| 33. C42×C97 | C2×C4 | semidirect |
| 73. C2×C97 | #354 | semidirect |
| 78. C97 | C2×#354 | semidirect |
| 89. C2×C42 | #87604 | semidirect |
| 111. C42 | C2×#87604 | semidirect |
| 153. C2 | #20261642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690869 | 2 |
| #20261642 | 2 |
| C2×#15690798 | 2 |
| C2×#354 | 97 |