Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 5. C4×#11715906 | C4 | semidirect |
| 18. C4×#87604 | C8 | semidirect |
| 22. C4×Dic97 | C8 | semidirect |
| 23. C4×Dic97 | C8 | semidirect |
| 24. C42×C97 | C8 | semidirect |
| 60. C97 | #1744 | semidirect |
| 84. C42 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C42×#87604 | 2 |
| #1744 | 97 |