Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #20261698 | C2 | semidirect |
| 4. C2×C8×#87604 | C2 | semidirect |
| 5. #20261610 | C2 | semidirect |
| 6. #20261607 | C2 | semidirect |
| 12. #15690875 | C4 | semidirect |
| 13. #15690874 | C4 | semidirect |
| 14. #15690873 | C4 | semidirect |
| 15. #15690872 | C4 | semidirect |
| 22. #15690818 | C4 | semidirect |
| 23. #15690817 | C4 | semidirect |
| 25. #15690816 | C4 | semidirect |
| 30. #131×C97 | C4 | semidirect |
| 128. C97 | #1764 | semidirect |
| 142. #131 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#104 | 2 |
| #20261725 | 2 |
| #20261698 | 2 |
| C2×C8×#87604 | 2 |
| #20261610 | 2 |
| #20261607 | 2 |
| #131×D97 | 2 |
| #1764 | 97 |