Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 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 |
|---|---|---|
| 1. C2×D97⋊M16 | C2 | semidirect |
| 2. C2×#15690889 | C2 | semidirect |
| 3. #20261727 | C2 | direct (N × H) |
| 4. C2×#15690872 | C2 | semidirect |
| 8. D97⋊M16 | C22 | semidirect |
| 10. C2×#13095519 | C22 | semidirect |
| 12. #15690889 | C22 | semidirect |
| 13. C2×C4⋊#87604 | C22 | semidirect |
| 16. #15690872 | C22 | semidirect |
| 18. C22×D388 | C4 | semidirect |
| 24. C2×D4×D97 | C4 | semidirect |
| 25. C2×D4×D97 | C4 | semidirect |
| 29. C22×D4×C97 | C4 | semidirect |
| 34. #13095519 | C23 | semidirect |
| 37. C4⋊#87604 | C23 | semidirect |
| 50. C2×D388 | C2×C4 | semidirect |
| 63. D4×D97 | C2×C4 | semidirect |
| 78. C2×D4×C97 | C2×C4 | semidirect |
| 157. C2×C97 | #418 | semidirect |
| 161. D97 | #418 | semidirect |
| 164. C97 | C2×#418 | semidirect |
| 181. C22×D4 | #87604 | semidirect |
| 223. C2×D4 | C2×#87604 | semidirect |
| 325. C2 | #20261727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C2×#15690889 | 2 |
| #20261727 | 2 |
| C2×#15690872 | 2 |
| C22×D4×D97 | 2 |
| C2×#418 | 97 |