Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 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. C22×Q8×D101 | C2 | semidirect |
| 2. C2×#15692284 | C2 | semidirect |
| 4. #20265335 | C2 | semidirect |
| 5. #20265334 | C2 | semidirect |
| 6. #20265333 | C2 | semidirect |
| 7. #20265315 | C2 | semidirect |
| 8. #20265314 | C2 | semidirect |
| 9. #20265184 | C2 | semidirect |
| 10. #20265139 | C2 | semidirect |
| 11. #448×C101 | C2 | semidirect |
| 23. C2×Dic404 | C22 | semidirect |
| 24. C2×#13108064 | C22 | semidirect |
| 25. C2×#13108062 | C22 | semidirect |
| 35. #15692180 | C22 | semidirect |
| 36. #15692179 | C22 | semidirect |
| 37. #15692178 | C22 | semidirect |
| 41. C2×SD16×C101 | C22 | semidirect |
| 43. #103×C101 | C22 | semidirect |
| 59. Q8×D101 | D4 | semidirect |
| 144. C22×C101 | #137 | semidirect |
| 152. C2×D101 | #137 | semidirect |
| 170. C101 | #3004 | semidirect |
| 179. #448 | D101 | semidirect |
| 197. C2×SD16 | C2×D101 | semidirect |
| 211. #103 | C2×D101 | semidirect |
| 321. C22 | #15692284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D101 | 2 |
| C2×#15692284 | 2 |
| #20265687 | 2 |
| #20265335 | 2 |
| #20265334 | 2 |
| #20265333 | 2 |
| #20265315 | 2 |
| #20265314 | 2 |
| #20265184 | 2 |
| #20265139 | 2 |
| #448×C101 | 2 |
| #3004 | 101 |