Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C4⋊C4×Dic97 | C2 | semidirect |
| 4. C4×#13095488 | C2 | semidirect |
| 5. #20260582 | C2 | semidirect |
| 6. #20260581 | C2 | semidirect |
| 7. #95×D97 | C2 | semidirect |
| 8. C4×C4⋊C4×C97 | C2 | semidirect |
| 12. C4×D388 | C4 | semidirect |
| 13. #15690772 | C4 | semidirect |
| 36. C2×C4×D97 | C2×C4 | semidirect |
| 37. C2×C4×D97 | C2×C4 | semidirect |
| 38. C4⋊Dic97 | C2×C4 | semidirect |
| 39. #13095488 | C2×C4 | semidirect |
| 40. #13095488 | C2×C4 | semidirect |
| 42. C4×Dic97 | C2×C4 | semidirect |
| 47. C4⋊C4×C97 | C2×C4 | semidirect |
| 49. C42×C97 | C2×C4 | semidirect |
| 74. D388 | C42 | semidirect |
| 101. C97 | #2275 | semidirect |
| 105. C4×C4⋊C4 | D97 | semidirect |
| 144. C4⋊C4 | C4×D97 | semidirect |
| 150. C42 | 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×#15690772 | 2 |
| C4⋊C4×Dic97 | 2 |
| C4×#13095488 | 2 |
| #20260582 | 2 |
| #20260581 | 2 |
| #95×D97 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2275 | 97 |