Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#15692302 | C2 | semidirect |
| 2. C2×#15692288 | C2 | semidirect |
| 3. C2×#15692275 | C2 | semidirect |
| 4. #20265758 | C2 | semidirect |
| 5. #20265340 | C2 | semidirect |
| 6. #20265334 | C2 | semidirect |
| 7. #20265323 | C2 | semidirect |
| 8. #20265317 | C2 | semidirect |
| 9. C2×#15692178 | C2 | semidirect |
| 10. #20265145 | C2 | semidirect |
| 11. #417×C101 | C2 | semidirect |
| 58. C2×Dic202 | D4 | semidirect |
| 87. #41×C101 | D4 | semidirect |
| 170. C101 | #3013 | semidirect |
| 179. #417 | D101 | semidirect |
| 224. #41 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C2×#15692288 | 2 |
| C2×#15692275 | 2 |
| #20265758 | 2 |
| #20265340 | 2 |
| #20265334 | 2 |
| #20265323 | 2 |
| #20265317 | 2 |
| C2×#15692178 | 2 |
| #20265145 | 2 |
| #417×C101 | 2 |
| #3013 | 101 |