Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20265217 | C2 | semidirect |
| 5. #20264946 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 7. #384×C101 | C2 | semidirect |
| 19. #15692183 | C4 | semidirect |
| 38. #13108058 | C2×C4 | semidirect |
| 58. C42×C101 | C2×C4 | semidirect |
| 80. D404 | C4⋊C4 | semidirect |
| 85. Dic202 | C4⋊C4 | semidirect |
| 113. C101 | #1859 | semidirect |
| 118. #384 | D101 | semidirect |
| 171. C42 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265658 | 2 |
| #20265217 | 2 |
| C2×#15692183 | 2 |
| #20265176 | 2 |
| #20264946 | 2 |
| #20264937 | 2 |
| #384×C101 | 2 |
| #1859 | 101 |