Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15690835 | C2 | semidirect |
| 2. C2×#15690835 | C2 | semidirect |
| 3. #20261502 | C2 | semidirect |
| 4. #20261003 | C2 | semidirect |
| 5. #20261000 | C2 | semidirect |
| 6. #20260783 | C2 | semidirect |
| 7. #20260719 | C2 | semidirect |
| 8. C2×#15690726 | C2 | semidirect |
| 9. #575×C97 | C2 | semidirect |
| 16. C2×#13095498 | C22 | semidirect |
| 18. C2×#13095496 | C22 | semidirect |
| 20. #15690817 | C22 | semidirect |
| 25. #15690745 | C22 | semidirect |
| 26. #15690729 | C22 | semidirect |
| 27. #15690727 | C22 | semidirect |
| 28. #15690726 | C22 | semidirect |
| 32. #137×C97 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C97 | C22 | semidirect |
| 148. C97 | #3068 | semidirect |
| 149. #575 | D97 | semidirect |
| 162. #137 | C2×D97 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| #20261502 | 2 |
| #20261003 | 2 |
| #20261000 | 2 |
| #20260783 | 2 |
| #20260719 | 2 |
| C2×#15690726 | 2 |
| #575×C97 | 2 |
| #3068 | 97 |