Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692281 | C2 | semidirect |
| 2. C4×#13108074 | C2 | semidirect |
| 3. #20265374 | C2 | semidirect |
| 4. #20265369 | C2 | semidirect |
| 5. #20265201 | C2 | semidirect |
| 6. #20265182 | C2 | semidirect |
| 7. C2×#127×C101 | C2 | semidirect |
| 10. C2×#13108062 | C22 | semidirect |
| 11. C2×#13108059 | C22 | semidirect |
| 13. C4×Dic202 | C22 | semidirect |
| 14. C4×D404 | C22 | semidirect |
| 19. C4⋊#11717579 | C22 | semidirect |
| 20. #15692176 | C22 | semidirect |
| 28. #13108074 | D4 | semidirect |
| 78. D404 | C2×D4 | semidirect |
| 82. Dic202 | C2×D4 | semidirect |
| 94. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 105. C101 | #3038 | semidirect |
| 107. C2×#127 | D101 | semidirect |
| 201. C4 | #15692281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| C4×#13108074 | 2 |
| #20265374 | 2 |
| #20265369 | 2 |
| #20265201 | 2 |
| #20265182 | 2 |
| C2×#127×C101 | 2 |
| #3038 | 101 |