Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4⋊C4×D97 | C2 | semidirect |
| 3. #20261047 | C2 | direct (N × H) |
| 4. C2×#15690744 | C2 | semidirect |
| 5. C2×#15690743 | C2 | semidirect |
| 6. C2×#15690731 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C2×#102×C97 | C2 | semidirect |
| 19. C4⋊C4×D97 | C22 | semidirect |
| 21. #15690744 | C22 | semidirect |
| 22. #15690743 | C22 | semidirect |
| 23. #15690731 | C22 | semidirect |
| 24. #15690722 | C22 | semidirect |
| 28. #102×C97 | C22 | semidirect |
| 111. C2×C97 | #480 | semidirect |
| 117. C97 | C2×#480 | semidirect |
| 124. C2×#102 | D97 | semidirect |
| 144. #102 | C2×D97 | semidirect |
| 229. C2 | #20261047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690781 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #20261047 | 2 |
| C2×#15690744 | 2 |
| C2×#15690743 | 2 |
| C2×#15690731 | 2 |
| C2×#15690722 | 2 |
| C2×#102×C97 | 2 |
| C2×#480 | 97 |