Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D101 | C2 | semidirect |
| 3. #20265619 | C2 | direct (N × H) |
| 4. C2×#15692201 | C2 | semidirect |
| 5. C2×#15692200 | C2 | semidirect |
| 6. C2×#15692198 | C2 | semidirect |
| 7. C2×#15692194 | C2 | semidirect |
| 8. C2×Q32×C101 | C2 | semidirect |
| 16. Q16×D101 | C22 | semidirect |
| 20. #15692201 | C22 | semidirect |
| 21. #15692200 | C22 | semidirect |
| 22. #15692198 | C22 | semidirect |
| 23. #15692194 | C22 | semidirect |
| 27. Q32×C101 | C22 | semidirect |
| 93. C2×C101 | #510 | semidirect |
| 98. C101 | C2×#510 | semidirect |
| 103. C2×Q32 | D101 | semidirect |
| 121. Q32 | C2×D101 | semidirect |
| 193. C2 | #20265619 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×Q16×D101 | 2 |
| #20265619 | 2 |
| C2×#15692201 | 2 |
| C2×#15692200 | 2 |
| C2×#15692198 | 2 |
| C2×#15692194 | 2 |
| C2×Q32×C101 | 2 |
| C2×#510 | 101 |