Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 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. #20260858 | C2 | direct (N × H) |
| 4. C2×#15690746 | C2 | semidirect |
| 5. C2×#15690738 | C2 | semidirect |
| 6. C2×#97×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. #97×C97 | C22 | semidirect |
| 32. Dic388 | C2×C4 | semidirect |
| 33. #13095500 | C2×C4 | semidirect |
| 34. D776 | C2×C4 | semidirect |
| 88. C2×C97 | #444 | semidirect |
| 92. C97 | C2×#444 | semidirect |
| 98. C2×#97 | D97 | semidirect |
| 115. #97 | C2×D97 | semidirect |
| 181. C2 | #20260858 | 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 |
| #20260858 | 2 |
| C2×#15690746 | 2 |
| C2×#15690738 | 2 |
| C2×#97×C97 | 2 |
| C2×#444 | 97 |