Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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×#15690816 | C2 | semidirect |
| 3. #20260853 | C2 | direct (N × H) |
| 4. C2×#15690746 | C2 | semidirect |
| 5. C2×#15690738 | C2 | semidirect |
| 6. C2×C4×C8×C97 | C2 | semidirect |
| 8. #15690832 | C4 | semidirect |
| 10. C2×Dic388 | C4 | semidirect |
| 11. C2×#13095500 | C4 | semidirect |
| 12. C2×D776 | C4 | semidirect |
| 14. #15690816 | C22 | semidirect |
| 18. #15690746 | C22 | semidirect |
| 19. #15690738 | C22 | semidirect |
| 23. C4×C8×C97 | C22 | semidirect |
| 32. Dic388 | C2×C4 | semidirect |
| 33. #13095500 | C2×C4 | semidirect |
| 34. D776 | C2×C4 | semidirect |
| 90. C2×C97 | #443 | semidirect |
| 94. C97 | C2×#443 | semidirect |
| 100. C2×C4×C8 | D97 | semidirect |
| 117. C4×C8 | C2×D97 | semidirect |
| 185. C2 | #20260853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690816 | 2 |
| #20260853 | 2 |
| C2×#15690746 | 2 |
| C2×#15690738 | 2 |
| C2×C4×C8×C97 | 2 |
| C2×#443 | 97 |