Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D97 | C2 | semidirect |
| 2. C2×D1552 | C2 | semidirect |
| 3. C2×#15690751 | C2 | semidirect |
| 4. #20260972 | C2 | semidirect |
| 5. #20260535 | C2 | semidirect |
| 6. #20260514 | C2 | semidirect |
| 7. #357×C97 | C2 | semidirect |
| 10. C2×D776 | C22 | semidirect |
| 18. C2×#13095486 | C22 | semidirect |
| 21. C2×C16×C97 | C22 | semidirect |
| 22. #107×C97 | C22 | semidirect |
| 34. D776 | D4 | semidirect |
| 43. D8×C97 | D4 | semidirect |
| 83. C2×D97 | D16 | semidirect |
| 96. C97 | #2184 | semidirect |
| 102. #357 | D97 | semidirect |
| 116. C2×C16 | C2×D97 | semidirect |
| 117. #107 | C2×D97 | semidirect |
| 134. D8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D97 | 2 |
| C2×D1552 | 2 |
| C2×#15690751 | 2 |
| #20260972 | 2 |
| #20260535 | 2 |
| #20260514 | 2 |
| #357×C97 | 2 |
| #2184 | 97 |