Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#15692320 | C2 | semidirect |
| 2. C4×#13108084 | C2 | semidirect |
| 3. C4×C4⋊#87938 | C2 | semidirect |
| 13. #15692252 | C4 | semidirect |
| 14. #15692244 | C4 | semidirect |
| 20. C4⋊Q8×C101 | C4 | semidirect |
| 23. #13108084 | D4 | semidirect |
| 81. C4×C101 | #104 | semidirect |
| 93. C101 | #1980 | semidirect |
| 100. C4⋊Q8 | #87938 | semidirect |
| 177. C4 | #15692320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692320 | 2 |
| C4×#13108084 | 2 |
| C4×C4⋊#87938 | 2 |
| #20265728 | 2 |
| #1980 | 101 |