Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20266013 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265352 | C2 | semidirect |
| 5. #20265347 | C2 | semidirect |
| 6. #20265193 | C2 | semidirect |
| 7. #413×C101 | C2 | semidirect |
| 8. #15692303 | C22 | semidirect |
| 12. #15692300 | C22 | semidirect |
| 16. C22×D404 | C22 | semidirect |
| 18. #15692283 | C22 | semidirect |
| 21. #15692251 | C22 | semidirect |
| 22. #15692244 | C22 | semidirect |
| 25. #15692214 | C22 | semidirect |
| 26. #15692181 | C22 | semidirect |
| 28. C2×M16×C101 | C22 | semidirect |
| 29. #101×C101 | C22 | semidirect |
| 30. #100×C101 | C22 | semidirect |
| 38. #13108074 | D4 | semidirect |
| 43. C2×Dic202 | D4 | semidirect |
| 49. C2×D404 | D4 | semidirect |
| 135. C101 | #3021 | semidirect |
| 142. #413 | D101 | semidirect |
| 157. C2×M16 | C2×D101 | semidirect |
| 164. #101 | C2×D101 | semidirect |
| 165. #100 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| C2×#15692283 | 2 |
| #20265741 | 2 |
| #20265352 | 2 |
| #20265347 | 2 |
| #20265193 | 2 |
| #413×C101 | 2 |
| #3021 | 101 |