Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#15692283 | C2 | semidirect |
| 3. C22×#13108061 | C2 | semidirect |
| 4. #20265746 | C2 | semidirect |
| 5. #20265325 | C2 | semidirect |
| 6. #20265317 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #20265145 | C2 | semidirect |
| 9. #419×C101 | C2 | semidirect |
| 13. C2×#13108075 | C22 | semidirect |
| 18. C2×Q8×D101 | C22 | semidirect |
| 30. #15692178 | C22 | semidirect |
| 31. #15692175 | C22 | semidirect |
| 32. #15692167 | C22 | semidirect |
| 36. #103×C101 | C22 | semidirect |
| 45. #13108074 | D4 | semidirect |
| 74. C2×Q8×C101 | D4 | semidirect |
| 146. C101 | #3010 | semidirect |
| 153. #419 | D101 | semidirect |
| 180. #103 | C2×D101 | semidirect |
| 200. 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×#15692283 | 2 |
| C22×#13108061 | 2 |
| #20265746 | 2 |
| #20265325 | 2 |
| #20265317 | 2 |
| #20265171 | 2 |
| #20265145 | 2 |
| #419×C101 | 2 |
| #3010 | 101 |