Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
612 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 12. (C2×#87604)⋊C4 | C4 | semidirect |
| 16. C2×C4⋊Dic97 | C4 | semidirect |
| 17. C2×#13095490 | C4 | semidirect |
| 18. C2×#13095490 | C4 | semidirect |
| 21. C2×C4⋊C4×C97 | C4 | semidirect |
| 82. C2×#87604 | C4⋊C4 | semidirect |
| 88. C2×C4×C97 | C42 | semidirect |
| 95. C2×Dic97 | C42 | semidirect |
| 144. C97 | #1436 | semidirect |
| 160. C2×C4⋊C4 | #87604 | semidirect |
| 247. C2×C4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#87604 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #1436 | 97 |