Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C2×#15690867 | C2 | semidirect |
| 2. C2×(C2×#87604)⋊C4 | C2 | semidirect |
| 3. #20261587 | C2 | direct (N × H) |
| 8. #15690867 | C22 | semidirect |
| 10. (C2×#87604)⋊C4 | C22 | semidirect |
| 12. C22×D388 | C4 | semidirect |
| 16. #15690785 | C4 | semidirect |
| 19. C2×C4⋊C4×C97 | C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 46. C4⋊C4×C97 | C2×C4 | semidirect |
| 103. C2×C97 | #327 | semidirect |
| 112. C97 | C2×#327 | semidirect |
| 126. C2×C4⋊C4 | #87604 | semidirect |
| 156. C4⋊C4 | C2×#87604 | semidirect |
| 219. C2 | #20261587 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690867 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #20261587 | 2 |
| C2×#15690785 | 2 |
| C2×#327 | 97 |