Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 7. #15690867 | C4 | semidirect |
| 9. (C2×#87604)⋊C4 | C4 | semidirect |
| 11. C2×C4⋊Dic97 | C4 | semidirect |
| 14. C2×C4⋊C4×C97 | C4 | semidirect |
| 119. C97 | #1294 | semidirect |
| 127. C2×C4⋊C4 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690867 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #20260592 | 2 |
| #1294 | 97 |