Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 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. #20265132 | C2 | semidirect |
| 5. #20264949 | C2 | semidirect |
| 6. #20264947 | C2 | semidirect |
| 7. #405×C101 | C2 | semidirect |
| 15. C2×#13108057 | C4 | semidirect |
| 16. C2×C8×D101 | C4 | semidirect |
| 18. #15692173 | C4 | semidirect |
| 19. #15692171 | C4 | semidirect |
| 107. C101 | #1757 | semidirect |
| 112. #405 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265159 | 2 |
| #20265150 | 2 |
| #20265132 | 2 |
| #20264949 | 2 |
| #20264947 | 2 |
| #405×C101 | 2 |
| #1757 | 101 |