Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690801 | C2 | semidirect |
| 3. #20261098 | C2 | direct (N × H) |
| 4. C2×#15690732 | C2 | semidirect |
| 5. C2×#15690731 | C2 | semidirect |
| 6. C2×#15690730 | C2 | semidirect |
| 7. C2×#15690720 | C2 | semidirect |
| 8. C2×#102×C97 | C2 | semidirect |
| 16. #15690801 | C22 | semidirect |
| 21. #15690732 | C22 | semidirect |
| 22. #15690731 | C22 | semidirect |
| 23. #15690730 | C22 | semidirect |
| 24. #15690720 | C22 | semidirect |
| 28. #102×C97 | C22 | semidirect |
| 111. C2×C97 | #490 | semidirect |
| 117. C97 | C2×#490 | semidirect |
| 124. C2×#102 | D97 | semidirect |
| 144. #102 | C2×D97 | semidirect |
| 229. C2 | #20261098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| C2×#15690801 | 2 |
| #20261098 | 2 |
| C2×#15690732 | 2 |
| C2×#15690731 | 2 |
| C2×#15690730 | 2 |
| C2×#15690720 | 2 |
| C2×#102×C97 | 2 |
| C2×#490 | 97 |