Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#15690744 | C2 | semidirect |
| 5. #20260633 | C2 | semidirect |
| 6. #20260498 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 19. #15690732 | C4 | semidirect |
| 41. C4⋊Dic97 | C2×C4 | semidirect |
| 53. C2×C8×C97 | C2×C4 | semidirect |
| 88. D388 | C4⋊C4 | semidirect |
| 124. C97 | #1862 | semidirect |
| 131. #336 | D97 | semidirect |
| 169. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C2×#15690744 | 2 |
| C2×#15690732 | 2 |
| #20260633 | 2 |
| #20260498 | 2 |
| #336×C97 | 2 |
| #1862 | 97 |