Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
696 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 290 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. C4⋊C4×#87604 | C2 | semidirect |
| 5. #15690889 | C4 | semidirect |
| 13. C2×C4⋊Dic97 | C4 | semidirect |
| 14. C2×#13095490 | C4 | semidirect |
| 15. C4⋊C4×D97 | C4 | semidirect |
| 17. C2×C4⋊C4×C97 | C4 | semidirect |
| 19. C4⋊#87604 | C2×C4 | semidirect |
| 22. C4×#87604 | C2×C4 | semidirect |
| 47. C2×C4×C97 | C42 | semidirect |
| 51. C2×Dic97 | C42 | semidirect |
| 56. C4×D97 | C42 | semidirect |
| 82. C97 | #2274 | semidirect |
| 95. C2×C4⋊C4 | #87604 | semidirect |
| 138. 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 |
| C4⋊C4×#87604 | 2 |
| C4×C22⋊#87604 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #2274 | 97 |