Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 762 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. C2×#15692300 | C2 | semidirect |
| 2. #20265977 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265357 | C2 | semidirect |
| 5. #20265347 | C2 | semidirect |
| 6. #20265193 | C2 | semidirect |
| 7. C2×#100×C101 | C2 | semidirect |
| 12. C2×#13108074 | C22 | semidirect |
| 17. #15692288 | C22 | semidirect |
| 19. #15692283 | C22 | semidirect |
| 21. #15692251 | C22 | semidirect |
| 22. #15692242 | C22 | semidirect |
| 25. #15692214 | C22 | semidirect |
| 26. #15692181 | C22 | semidirect |
| 28. C2×M16×C101 | C22 | semidirect |
| 29. #100×C101 | C22 | semidirect |
| 35. #13108074 | D4 | semidirect |
| 39. C2×Dic202 | D4 | semidirect |
| 40. C2×Dic202 | C23 | semidirect |
| 41. C2×D404 | D4 | semidirect |
| 42. C2×D404 | C23 | semidirect |
| 61. C4×Dic101 | C23 | semidirect |
| 69. M16×C101 | C23 | semidirect |
| 132. C101 | #3019 | semidirect |
| 139. C2×#100 | D101 | semidirect |
| 154. C2×M16 | C2×D101 | semidirect |
| 161. #100 | C2×D101 | semidirect |
| 197. M16 | C22×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692300 | 2 |
| #20265977 | 2 |
| #20265744 | 2 |
| #20265357 | 2 |
| #20265347 | 2 |
| #20265193 | 2 |
| C2×#100×C101 | 2 |
| #3019 | 101 |