Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. M16×Dic101 | C2 | semidirect |
| 5. C42×Dic101 | C2 | semidirect |
| 6. #20264936 | C2 | semidirect |
| 7. #339×C101 | C2 | semidirect |
| 10. #15692220 | C4 | semidirect |
| 11. #15692217 | C4 | semidirect |
| 18. #15692183 | C4 | semidirect |
| 19. #15692181 | C4 | semidirect |
| 37. #13108058 | C2×C4 | semidirect |
| 45. C4×Dic101 | C2×C4 | semidirect |
| 51. M16×C101 | C2×C4 | semidirect |
| 57. C42×C101 | C2×C4 | semidirect |
| 78. D404 | C42 | semidirect |
| 83. Dic202 | C42 | semidirect |
| 101. Dic101 | #104 | semidirect |
| 108. C101 | C4×#104 | semidirect |
| 115. #339 | D101 | semidirect |
| 149. M16 | C4×D101 | semidirect |
| 165. C42 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265645 | 2 |
| C2×#15692183 | 2 |
| C2×#15692181 | 2 |
| M16×Dic101 | 2 |
| C42×Dic101 | 2 |
| #20264936 | 2 |
| #339×C101 | 2 |
| C4×#104 | 101 |