Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 3. #20261686 | C2 | semidirect |
| 5. C4×C4⋊#87604 | C2 | semidirect |
| 18. #15690769 | C4 | semidirect |
| 19. #15690768 | C4 | semidirect |
| 20. #15690767 | C4 | semidirect |
| 21. #15690766 | C4 | semidirect |
| 25. #117×C97 | C4 | semidirect |
| 45. C4⋊Dic97 | C2×C4 | semidirect |
| 46. #13095490 | C2×C4 | semidirect |
| 49. C4×Dic97 | C2×C4 | semidirect |
| 50. C4×Dic97 | C2×C4 | semidirect |
| 52. C4⋊C4×C97 | C2×C4 | semidirect |
| 54. C42×C97 | C2×C4 | semidirect |
| 67. C2×C4×C97 | C4⋊C4 | semidirect |
| 71. C2×Dic97 | C4⋊C4 | semidirect |
| 76. C4×D97 | C4⋊C4 | semidirect |
| 77. C4×D97 | C4⋊C4 | semidirect |
| 107. C97 | #2296 | semidirect |
| 121. #117 | #87604 | semidirect |
| 151. C4⋊C4 | C2×#87604 | semidirect |
| 161. C42 | C2×#87604 | semidirect |
| 185. 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×#15690889 | 2 |
| C22×C4×#87604 | 2 |
| #20261686 | 2 |
| #20261682 | 2 |
| C4×C4⋊#87604 | 2 |
| #117×D97 | 2 |
| #2296 | 97 |