Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265300 | C2 | semidirect |
| 4. #20265295 | C2 | semidirect |
| 5. #20265226 | C2 | semidirect |
| 6. #20265195 | C2 | semidirect |
| 7. #405×C101 | C2 | semidirect |
| 9. #15692288 | C4 | semidirect |
| 10. #15692283 | C4 | semidirect |
| 14. #15692261 | C22 | semidirect |
| 15. #15692261 | C22 | semidirect |
| 19. #15692191 | C22 | semidirect |
| 20. #15692183 | C22 | semidirect |
| 24. #97×C101 | C22 | semidirect |
| 25. C4×C8×C101 | C22 | semidirect |
| 90. C101 | #2955 | semidirect |
| 97. #405 | D101 | semidirect |
| 114. #97 | C2×D101 | semidirect |
| 115. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692261 | 2 |
| #20265300 | 2 |
| #20265295 | 2 |
| #20265226 | 2 |
| #20265195 | 2 |
| #405×C101 | 2 |
| #2955 | 101 |