Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 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. #20261682 | C2 | semidirect |
| 3. #20261677 | C2 | semidirect |
| 6. C2×C4⋊#87604 | C22 | semidirect |
| 10. (C2×#87604)⋊C4 | C22 | semidirect |
| 13. C2×C22⋊Dic97 | C4 | semidirect |
| 14. C2×#13095488 | C4 | semidirect |
| 15. C22⋊C4×D97 | C4 | semidirect |
| 17. C2×C22⋊C4×C97 | C4 | semidirect |
| 31. C22×Dic97 | C2×C4 | semidirect |
| 33. C2×C4×D97 | C2×C4 | semidirect |
| 35. C22⋊Dic97 | C2×C4 | semidirect |
| 36. #13095488 | C2×C4 | semidirect |
| 38. C22×C4×C97 | C2×C4 | semidirect |
| 39. C22⋊C4×C97 | C2×C4 | semidirect |
| 41. C23×C97 | C4⋊C4 | semidirect |
| 50. C22×D97 | C4⋊C4 | semidirect |
| 51. C22×D97 | C4⋊C4 | semidirect |
| 99. C97 | #2315 | semidirect |
| 115. C2×C22⋊C4 | #87604 | semidirect |
| 132. C22×C4 | C2×#87604 | semidirect |
| 138. C22⋊C4 | C2×#87604 | semidirect |
| 155. C23 | C4⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#87604 | 2 |
| #20261682 | 2 |
| #20261677 | 2 |
| C2×C22⋊C4×D97 | 2 |
| #2315 | 97 |