Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20265660 | C2 | semidirect |
| 3. #20265183 | C2 | semidirect |
| 4. #20265179 | C2 | semidirect |
| 5. #20265174 | C2 | semidirect |
| 6. C2×#15692177 | C2 | semidirect |
| 7. C2×#131×C101 | C2 | semidirect |
| 9. #15692301 | C4 | semidirect |
| 16. #15692214 | C22 | semidirect |
| 17. C2×C4⋊Dic101 | C22 | semidirect |
| 18. #15692180 | C22 | semidirect |
| 19. #15692180 | C22 | semidirect |
| 20. #15692177 | C22 | semidirect |
| 21. #15692177 | C22 | semidirect |
| 22. #15692177 | C22 | semidirect |
| 25. C2×M16×C101 | C22 | semidirect |
| 26. C22×C8×C101 | C22 | semidirect |
| 30. #13108074 | C2×C4 | semidirect |
| 34. C2×D404 | C2×C4 | semidirect |
| 98. C101 | #2897 | semidirect |
| 100. C2×#131 | D101 | semidirect |
| 114. C2×M16 | C2×D101 | semidirect |
| 115. C22×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692301 | 2 |
| #20265660 | 2 |
| #20265183 | 2 |
| #20265179 | 2 |
| #20265174 | 2 |
| C2×#15692177 | 2 |
| C2×#131×C101 | 2 |
| #2897 | 101 |