Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 8. #15690864 | C4 | direct (N × H) |
| 9. C4×#11715897 | C4 | semidirect |
| 12. C4×#11715895 | C4 | semidirect |
| 13. C8×Dic97 | C4 | semidirect |
| 14. C4×C8×C97 | C4 | semidirect |
| 37. #11715897 | C42 | semidirect |
| 38. C8×C97 | C42 | semidirect |
| 39. #11715895 | C42 | semidirect |
| 44. C4×C97 | #97 | semidirect |
| 46. Dic97 | #97 | semidirect |
| 52. C97 | C4×#97 | semidirect |
| 66. C4×C8 | #87604 | semidirect |
| 91. C8 | C4×#87604 | semidirect |
| 98. C4 | #15690864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690864 | 2 |
| C4×#13095519 | 2 |
| C42×#87604 | 2 |
| C4×C8×D97 | 2 |
| C4×#97 | 97 |