Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20265618 | C2 | semidirect |
| 3. C2×#15692198 | C2 | semidirect |
| 4. #20264989 | C2 | semidirect |
| 5. #20264983 | C2 | semidirect |
| 6. #20264961 | C2 | semidirect |
| 7. #473×C101 | C2 | semidirect |
| 18. #15692195 | C22 | semidirect |
| 19. C2×#13108049 | C22 | semidirect |
| 21. C2×Q16×C101 | C22 | semidirect |
| 23. #108×C101 | C22 | semidirect |
| 92. C101 | #2194 | semidirect |
| 96. #473 | D101 | semidirect |
| 106. C2×Q16 | C2×D101 | semidirect |
| 115. #108 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265982 | 2 |
| #20265618 | 2 |
| C2×#15692198 | 2 |
| #20264989 | 2 |
| #20264983 | 2 |
| #20264961 | 2 |
| #473×C101 | 2 |
| #2194 | 101 |