Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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. C22×C8×D101 | C2 | semidirect |
| 3. #20265689 | C2 | semidirect |
| 4. #20265419 | C2 | semidirect |
| 5. #20265414 | C2 | semidirect |
| 6. #20265407 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #427×C101 | C2 | semidirect |
| 12. C2×Dic404 | C22 | semidirect |
| 13. C2×#13108063 | C22 | semidirect |
| 14. C2×D808 | C22 | semidirect |
| 24. #15692178 | C22 | semidirect |
| 25. #15692175 | C22 | semidirect |
| 28. #107×C101 | C22 | semidirect |
| 29. #106×C101 | C22 | semidirect |
| 54. C2×C8×C101 | D4 | semidirect |
| 94. C2×D101 | #135 | semidirect |
| 107. C101 | #3050 | semidirect |
| 114. #427 | D101 | semidirect |
| 133. #107 | C2×D101 | semidirect |
| 134. #106 | C2×D101 | semidirect |
| 158. C2×C8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C22×C8×D101 | 2 |
| #20265689 | 2 |
| #20265419 | 2 |
| #20265414 | 2 |
| #20265407 | 2 |
| #20265171 | 2 |
| #427×C101 | 2 |
| #3050 | 101 |