Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20265200 | C2 | semidirect |
| 4. C4×#13108053 | C2 | semidirect |
| 5. #20264938 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 9. Q8×Dic101 | C4 | semidirect |
| 10. Q8×Dic101 | C4 | semidirect |
| 13. D4×Dic101 | C4 | semidirect |
| 14. D4×Dic101 | C4 | semidirect |
| 72. Q8×C101 | C4⋊C4 | semidirect |
| 76. D4×C101 | C4⋊C4 | semidirect |
| 124. Dic101 | #104 | semidirect |
| 132. C101 | #1806 | semidirect |
| 204. Q8 | #13108053 | semidirect |
| 208. D4 | #13108053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic101 | 2 |
| #20265200 | 2 |
| C2×#15692182 | 2 |
| C4×#13108053 | 2 |
| #20264938 | 2 |
| #20264937 | 2 |
| C2×#104×C101 | 2 |
| #1806 | 101 |