Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D101 | C2 | semidirect |
| 3. C2×#15692231 | C2 | semidirect |
| 4. #20265432 | C2 | semidirect |
| 5. #20265420 | C2 | semidirect |
| 6. #20265415 | C2 | semidirect |
| 7. #20265403 | C2 | semidirect |
| 8. #20265219 | C2 | semidirect |
| 9. #20265186 | C2 | semidirect |
| 10. #20265178 | C2 | semidirect |
| 11. C2×#137×C101 | C2 | semidirect |
| 33. #15692189 | C22 | semidirect |
| 34. #15692187 | C22 | semidirect |
| 35. #15692179 | C22 | semidirect |
| 36. #15692179 | C22 | semidirect |
| 37. #15692179 | C22 | semidirect |
| 38. #15692176 | C22 | semidirect |
| 42. C2×Q16×C101 | C22 | semidirect |
| 43. C2×SD16×C101 | C22 | semidirect |
| 90. M16×C101 | D4 | semidirect |
| 145. C2×D101 | #137 | semidirect |
| 164. C101 | #3056 | semidirect |
| 165. C2×#137 | D101 | semidirect |
| 180. C2×Q16 | C2×D101 | semidirect |
| 181. C2×SD16 | C2×D101 | semidirect |
| 236. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D101 | 2 |
| #20265684 | 2 |
| C2×#15692231 | 2 |
| #20265432 | 2 |
| #20265420 | 2 |
| #20265415 | 2 |
| #20265403 | 2 |
| #20265219 | 2 |
| #20265186 | 2 |
| #20265178 | 2 |
| C2×#137×C101 | 2 |
| #3056 | 101 |