Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. C2×#15690834 | C2 | semidirect |
| 2. #20261283 | C2 | semidirect |
| 3. #127×D97 | C2 | semidirect |
| 4. #20261123 | C2 | semidirect |
| 5. #20261111 | C2 | semidirect |
| 6. #20261108 | C2 | semidirect |
| 7. #20261107 | C2 | semidirect |
| 8. C4×#13095494 | C2 | semidirect |
| 9. #493×C97 | C2 | semidirect |
| 14. C2×#13095500 | C22 | semidirect |
| 15. C2×#13095499 | C22 | semidirect |
| 16. C2×#13095496 | C22 | semidirect |
| 18. #15690810 | C22 | semidirect |
| 22. #15690797 | C22 | semidirect |
| 26. #15690720 | C22 | semidirect |
| 27. C4×#11715895 | C22 | semidirect |
| 28. C2×D8×C97 | C22 | semidirect |
| 30. #127×C97 | C22 | semidirect |
| 31. C4×C8×C97 | C22 | semidirect |
| 48. #13095494 | D4 | semidirect |
| 85. C8×C97 | C2×D4 | semidirect |
| 86. #11715895 | C2×D4 | semidirect |
| 97. C4×C97 | AGL(1,ℤ/8) | semidirect |
| 109. C97 | #3151 | semidirect |
| 115. #493 | D97 | semidirect |
| 126. C2×D8 | C2×D97 | semidirect |
| 133. #127 | C2×D97 | semidirect |
| 140. C4×C8 | C2×D97 | semidirect |
| 195. C8 | D4×D97 | semidirect |
| 209. C4 | #15690834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690834 | 2 |
| #20261283 | 2 |
| #127×D97 | 2 |
| #20261123 | 2 |
| #20261111 | 2 |
| #20261108 | 2 |
| #20261107 | 2 |
| C4×#13095494 | 2 |
| #493×C97 | 2 |
| #3151 | 97 |