Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#15690817 | C2 | semidirect |
| 2. #20261218 | C2 | semidirect |
| 3. #20260740 | C2 | semidirect |
| 4. #20260736 | C2 | semidirect |
| 5. #20260731 | C2 | semidirect |
| 6. C2×#15690731 | C2 | semidirect |
| 9. C2×#13095495 | C22 | semidirect |
| 10. C22×#11715895 | C22 | semidirect |
| 13. #15690769 | C22 | semidirect |
| 14. C2×C4⋊Dic97 | C22 | semidirect |
| 15. #15690734 | C22 | semidirect |
| 16. #15690734 | C22 | semidirect |
| 17. #15690731 | C22 | semidirect |
| 18. #15690731 | C22 | semidirect |
| 19. #15690731 | C22 | semidirect |
| 21. H(5,𝔽2)×C97 | C4 | semidirect |
| 41. #41×C97 | C2×C4 | semidirect |
| 49. C2×D4×C97 | C2×C4 | semidirect |
| 98. C97 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic97 | semidirect |
| 129. #41 | C2×Dic97 | semidirect |
| 137. C2×D4 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| #20261218 | 2 |
| #20260740 | 2 |
| #20260736 | 2 |
| #20260731 | 2 |
| C2×#15690731 | 2 |
| C2×H(5,𝔽2)×C97 | 2 |
| #2897 | 97 |