Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #20266256 | C2 | semidirect |
| 2. #41×#87938 | C2 | semidirect |
| 3. #20266175 | C2 | semidirect |
| 4. #20266174 | C2 | semidirect |
| 5. D101⋊#104 | C2 | semidirect |
| 6. C2×#15692319 | C2 | semidirect |
| 10. C2×#13108084 | C22 | semidirect |
| 11. D101⋊M16 | C22 | semidirect |
| 14. #15692334 | C22 | semidirect |
| 15. C2×C4×#87938 | C22 | semidirect |
| 16. #15692320 | C22 | semidirect |
| 17. #15692320 | C22 | semidirect |
| 18. #15692319 | C22 | semidirect |
| 19. #15692319 | C22 | semidirect |
| 20. #15692319 | C22 | semidirect |
| 22. #15692302 | C4 | semidirect |
| 23. #15692302 | C4 | semidirect |
| 25. #15692300 | C4 | semidirect |
| 31. H(5,𝔽2)×C101 | C4 | semidirect |
| 49. #13108074 | C2×C4 | semidirect |
| 56. #13108073 | C2×C4 | semidirect |
| 60. C2×Dic202 | C2×C4 | semidirect |
| 62. Q8×D101 | C2×C4 | semidirect |
| 68. D4×D101 | C2×C4 | semidirect |
| 75. #41×C101 | C2×C4 | semidirect |
| 77. C2×D4×C101 | C2×C4 | semidirect |
| 140. C101 | #2901 | semidirect |
| 153. H(5,𝔽2) | #87938 | semidirect |
| 189. #41 | C2×#87938 | semidirect |
| 202. C2×D4 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266256 | 2 |
| #41×#87938 | 2 |
| #20266175 | 2 |
| #20266174 | 2 |
| D101⋊#104 | 2 |
| C2×#15692319 | 2 |
| #20266012 | 2 |
| #2901 | 101 |