Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D97⋊#131 | C2 | semidirect |
| 2. #20261804 | C2 | semidirect |
| 3. #20261727 | C2 | semidirect |
| 4. #20261726 | C2 | semidirect |
| 5. #20261725 | C2 | semidirect |
| 6. C2×#15690872 | C2 | semidirect |
| 10. D97⋊M16 | C22 | semidirect |
| 11. C2×#13095519 | C22 | semidirect |
| 14. #15690889 | C22 | semidirect |
| 15. C2×C4⋊#87604 | C22 | semidirect |
| 16. #15690873 | C22 | semidirect |
| 17. #15690873 | C22 | semidirect |
| 18. #15690872 | C22 | semidirect |
| 19. #15690872 | C22 | semidirect |
| 20. #15690872 | C22 | semidirect |
| 22. #15690856 | C4 | semidirect |
| 23. #15690856 | C4 | semidirect |
| 25. #15690855 | C4 | semidirect |
| 31. H(5,𝔽2)×C97 | C4 | semidirect |
| 46. #13095512 | C2×C4 | semidirect |
| 51. #13095511 | C2×C4 | semidirect |
| 54. #13095510 | C2×C4 | semidirect |
| 59. C2×D388 | C2×C4 | semidirect |
| 68. D4×D97 | C2×C4 | semidirect |
| 75. #41×C97 | C2×C4 | semidirect |
| 77. C2×D4×C97 | C2×C4 | semidirect |
| 147. C97 | #2897 | semidirect |
| 160. H(5,𝔽2) | #87604 | semidirect |
| 193. #41 | C2×#87604 | semidirect |
| 210. C2×D4 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#131 | 2 |
| #20261804 | 2 |
| #20261727 | 2 |
| #20261726 | 2 |
| #20261725 | 2 |
| C2×#15690872 | 2 |
| H(5,𝔽2)×D97 | 2 |
| #2897 | 97 |