Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#15692277 | C2 | semidirect |
| 2. #20265688 | C2 | semidirect |
| 3. #20265418 | C2 | semidirect |
| 4. #20265413 | C2 | semidirect |
| 5. #20265406 | C2 | semidirect |
| 6. #20265215 | C2 | semidirect |
| 7. #20265174 | C2 | semidirect |
| 8. C23×C8×C101 | C2 | semidirect |
| 11. C2×Dic404 | C22 | semidirect |
| 12. C2×#13108063 | C22 | semidirect |
| 13. C2×D808 | C22 | semidirect |
| 20. #15692189 | C22 | semidirect |
| 21. #15692187 | C22 | semidirect |
| 22. #15692180 | C22 | semidirect |
| 23. #15692177 | C22 | semidirect |
| 56. C2×C8×C101 | D4 | semidirect |
| 91. C22×C101 | #135 | semidirect |
| 107. C101 | #3050 | semidirect |
| 109. C23×C8 | D101 | semidirect |
| 157. C2×C8 | C22⋊D101 | semidirect |
| 200. C22 | #15692277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| #20265688 | 2 |
| #20265418 | 2 |
| #20265413 | 2 |
| #20265406 | 2 |
| #20265215 | 2 |
| #20265174 | 2 |
| C23×C8×C101 | 2 |
| #3050 | 101 |