Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
444 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 21. Q8×Dic101 | C4 | semidirect |
| 22. C4×Dic202 | C4 | semidirect |
| 23. C4×Dic202 | C4 | semidirect |
| 24. #15692220 | C4 | semidirect |
| 25. #15692220 | C4 | semidirect |
| 30. C4×Q8×C101 | C4 | semidirect |
| 116. C101 | #2320 | semidirect |
| 131. C4×Q8 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#87938)⋊Q8 | 2 |
| #20266128 | 2 |
| #20266126 | 2 |
| #20266122 | 2 |
| #20266121 | 2 |
| C4×C4⋊#87938 | 2 |
| #20266113 | 2 |
| C4×Q8×D101 | 2 |
| #2320 | 101 |