Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #20266217 | C2 | direct (N × H) |
| 18. C2×Dic404 | C4 | semidirect |
| 19. C2×#13108064 | C4 | semidirect |
| 20. Q16×D101 | C4 | semidirect |
| 23. C2×Q16×C101 | C4 | semidirect |
| 43. Dic404 | C2×C4 | semidirect |
| 44. #13108064 | C2×C4 | semidirect |
| 49. Q16×C101 | C2×C4 | semidirect |
| 87. C2×C101 | #441 | semidirect |
| 89. D101 | #441 | semidirect |
| 92. C101 | C2×#441 | semidirect |
| 104. C2×Q16 | #87938 | semidirect |
| 129. Q16 | C2×#87938 | semidirect |
| 181. C2 | #20266217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87938 | 2 |
| #20266217 | 2 |
| C2×#15692323 | 2 |
| C2×#15692318 | 2 |
| C2×#15692309 | 2 |
| C2×Q16×D101 | 2 |
| C2×#441 | 101 |