Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#15690857 | C2 | semidirect |
| 2. #20261552 | C2 | direct (N × H) |
| 3. C2×#15690843 | C2 | semidirect |
| 4. C2×#15690832 | C2 | semidirect |
| 5. C22×Dic388 | C2 | semidirect |
| 6. C2×#131×C97 | C2 | semidirect |
| 8. #15690857 | C22 | semidirect |
| 13. #15690843 | C22 | semidirect |
| 14. #15690832 | C22 | semidirect |
| 17. C2×Dic388 | C22 | semidirect |
| 21. #131×C97 | C22 | semidirect |
| 78. C2×C97 | #578 | semidirect |
| 82. C97 | C2×#578 | semidirect |
| 88. C2×#131 | D97 | semidirect |
| 103. #131 | C2×D97 | semidirect |
| 161. C2 | #20261552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| #20261552 | 2 |
| C2×#15690843 | 2 |
| C2×#15690832 | 2 |
| C22×Dic388 | 2 |
| C2×#131×C97 | 2 |
| C2×#578 | 97 |