Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
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. D101⋊#131 | C2 | semidirect |
| 2. #20266246 | C2 | semidirect |
| 3. #20266169 | C2 | semidirect |
| 4. #20266168 | C2 | semidirect |
| 5. #20266167 | C2 | semidirect |
| 6. C2×#15692317 | C2 | semidirect |
| 10. D101⋊M16 | C22 | semidirect |
| 11. C2×D101⋊C8 | C22 | semidirect |
| 14. #15692334 | C22 | semidirect |
| 15. C2×C4⋊#87938 | C22 | semidirect |
| 16. #15692318 | C22 | semidirect |
| 17. #15692318 | C22 | semidirect |
| 18. #15692317 | C22 | semidirect |
| 19. #15692317 | C22 | semidirect |
| 20. #15692317 | C22 | semidirect |
| 22. #15692301 | C4 | semidirect |
| 23. #15692301 | C4 | semidirect |
| 25. #15692300 | C4 | semidirect |
| 31. H(5,𝔽2)×C101 | C4 | semidirect |
| 46. #13108075 | C2×C4 | semidirect |
| 51. #13108074 | C2×C4 | semidirect |
| 54. #13108073 | C2×C4 | semidirect |
| 59. C2×D404 | C2×C4 | semidirect |
| 68. D4×D101 | C2×C4 | semidirect |
| 75. #41×C101 | C2×C4 | semidirect |
| 77. C2×D4×C101 | C2×C4 | semidirect |
| 147. C101 | #2897 | semidirect |
| 160. H(5,𝔽2) | #87938 | semidirect |
| 193. #41 | C2×#87938 | semidirect |
| 210. C2×D4 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊#131 | 2 |
| #20266246 | 2 |
| #20266169 | 2 |
| #20266168 | 2 |
| #20266167 | 2 |
| C2×#15692317 | 2 |
| H(5,𝔽2)×D101 | 2 |
| #2897 | 101 |