Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
552 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 214 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 |
|---|---|---|
| 14. Q8×Dic101 | C4 | semidirect |
| 15. C4×Dic202 | C4 | semidirect |
| 16. #15692220 | C4 | semidirect |
| 19. C4×Q8×C101 | C4 | semidirect |
| 46. Q8×C101 | C4⋊C4 | semidirect |
| 57. Dic202 | C4⋊C4 | semidirect |
| 77. C101 | #2351 | semidirect |
| 88. C4×Q8 | #87938 | semidirect |
| 118. Q8 | C4⋊#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87938 | 2 |
| #20266128 | 2 |
| #20266121 | 2 |
| C4×C4⋊#87938 | 2 |
| C4×Q8×D101 | 2 |
| #2351 | 101 |