Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15692285 | C2 | semidirect |
| 4. #20265331 | C2 | semidirect |
| 5. #20265314 | C2 | semidirect |
| 6. #20265187 | C2 | semidirect |
| 7. #20265186 | C2 | semidirect |
| 8. #20265140 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 19. C2×#13108064 | C22 | semidirect |
| 20. C2×#13108062 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 29. #15692179 | C22 | semidirect |
| 34. C2×Q16×C101 | C22 | semidirect |
| 35. C2×SD16×C101 | C22 | semidirect |
| 42. C2×Dic202 | D4 | semidirect |
| 70. C2×Q8×C101 | D4 | semidirect |
| 127. C2×D101 | #137 | semidirect |
| 142. C101 | #3004 | semidirect |
| 145. C2×#137 | D101 | semidirect |
| 165. C2×Q16 | C2×D101 | semidirect |
| 167. C2×SD16 | C2×D101 | semidirect |
| 193. C2×Q8 | C22⋊D101 | 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×#15692285 | 2 |
| #20265684 | 2 |
| #20265331 | 2 |
| #20265314 | 2 |
| #20265187 | 2 |
| #20265186 | 2 |
| #20265140 | 2 |
| C2×#137×C101 | 2 |
| #3004 | 101 |