Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
680 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20261613 | C2 | direct (N × H) |
| 7. C2×C22⋊#87604 | C4 | semidirect |
| 10. C23×Dic97 | C4 | semidirect |
| 13. C2×#13095488 | C4 | semidirect |
| 15. C23×C4×C97 | C4 | semidirect |
| 22. C22⋊#87604 | C2×C4 | semidirect |
| 35. C22×Dic97 | C2×C4 | semidirect |
| 42. C22×C4×C97 | C2×C4 | semidirect |
| 119. C2×C97 | #342 | semidirect |
| 127. C97 | C2×#342 | semidirect |
| 134. C23×C4 | #87604 | semidirect |
| 164. C22×C4 | C2×#87604 | semidirect |
| 249. C2 | #20261613 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#87604 | 2 |
| #20261613 | 2 |
| C22×#13095488 | 2 |
| C2×#342 | 97 |