Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#15692262 | C2 | semidirect |
| 2. #20265299 | C2 | semidirect |
| 3. #20265294 | C2 | semidirect |
| 4. #20265226 | C2 | semidirect |
| 5. #20265194 | C2 | semidirect |
| 6. #20265135 | C2 | semidirect |
| 10. #15692262 | C22 | semidirect |
| 11. #15692262 | C22 | semidirect |
| 17. #15692191 | C22 | semidirect |
| 18. #15692182 | C22 | semidirect |
| 19. #15692165 | C22 | semidirect |
| 20. C8×Dic101 | C22 | semidirect |
| 22. #137×C101 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C101 | C4 | semidirect |
| 90. C101 | #2955 | semidirect |
| 99. #137 | Dic101 | semidirect |
| 100. AGL(1,ℤ/8) | Dic101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692262 | 2 |
| #20265299 | 2 |
| #20265294 | 2 |
| #20265226 | 2 |
| #20265194 | 2 |
| #20265135 | 2 |
| #575×C101 | 2 |
| #2955 | 101 |