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×#15692303 | C2 | semidirect |
| 2. C2×#15692286 | C2 | semidirect |
| 3. C2×#15692277 | C2 | semidirect |
| 4. #20265758 | C2 | semidirect |
| 5. #20265342 | C2 | semidirect |
| 6. #20265334 | C2 | semidirect |
| 7. #20265325 | C2 | semidirect |
| 8. #20265317 | C2 | semidirect |
| 9. #20265176 | C2 | semidirect |
| 10. #20265143 | C2 | semidirect |
| 11. C2×#103×C101 | C2 | semidirect |
| 54. #13108074 | D4 | semidirect |
| 88. C2×Q8×C101 | D4 | semidirect |
| 170. C101 | #3013 | semidirect |
| 180. C2×#103 | D101 | semidirect |
| 234. C2×Q8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692303 | 2 |
| C2×#15692286 | 2 |
| C2×#15692277 | 2 |
| #20265758 | 2 |
| #20265342 | 2 |
| #20265334 | 2 |
| #20265325 | 2 |
| #20265317 | 2 |
| #20265176 | 2 |
| #20265143 | 2 |
| C2×#103×C101 | 2 |
| #3013 | 101 |