Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
888 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 354 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 |
|---|---|---|
| 2. #20261681 | C2 | direct (N × H) |
| 8. C2×C4×Dic97 | C4 | semidirect |
| 9. C42×D97 | C4 | semidirect |
| 11. C2×C42×C97 | C4 | semidirect |
| 21. C4×Dic97 | C2×C4 | semidirect |
| 23. C42×C97 | C2×C4 | semidirect |
| 31. C2×C4×C97 | C4⋊C4 | semidirect |
| 33. C2×Dic97 | C4⋊C4 | semidirect |
| 35. C4×D97 | C4⋊C4 | semidirect |
| 46. C4×C97 | C2×C4⋊C4 | semidirect |
| 47. Dic97 | C2×C4⋊C4 | semidirect |
| 48. C2×C97 | #384 | semidirect |
| 50. D97 | #384 | semidirect |
| 54. C97 | C2×#384 | semidirect |
| 65. C2×C42 | #87604 | semidirect |
| 77. C42 | C2×#87604 | semidirect |
| 90. C2×C4 | C4⋊#87604 | semidirect |
| 101. C4 | C2×C4⋊#87604 | semidirect |
| 105. C2 | #20261681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| #20261681 | 2 |
| C2×C42×D97 | 2 |
| C2×#384 | 97 |