Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×#15690769 | C2 | semidirect |
| 3. #20260732 | C2 | direct (N × H) |
| 4. C2×#15690735 | C2 | semidirect |
| 5. C2×#15690732 | C2 | semidirect |
| 6. C23×C8×C97 | C2 | semidirect |
| 9. C2×#13095511 | C4 | semidirect |
| 16. #15690769 | C22 | semidirect |
| 20. #15690735 | C22 | semidirect |
| 21. #15690732 | C22 | semidirect |
| 25. C22×C8×C97 | C22 | semidirect |
| 29. #13095511 | C2×C4 | semidirect |
| 103. C2×C97 | #416 | semidirect |
| 108. C97 | C2×#416 | semidirect |
| 110. C23×C8 | D97 | semidirect |
| 126. C22×C8 | C2×D97 | semidirect |
| 212. C2 | #20260732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C2×#15690769 | 2 |
| #20260732 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C23×C8×C97 | 2 |
| C2×#416 | 97 |