Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692254 | C2 | semidirect |
| 3. #20265538 | C2 | direct (N × H) |
| 4. C2×#15692179 | C2 | semidirect |
| 7. C2×#15692165 | C2 | semidirect |
| 8. C2×#103×C101 | C2 | semidirect |
| 13. #15692254 | C22 | semidirect |
| 21. #15692179 | C22 | semidirect |
| 24. #15692165 | C22 | semidirect |
| 28. #103×C101 | C22 | semidirect |
| 103. C2×C101 | #489 | semidirect |
| 109. C101 | C2×#489 | semidirect |
| 114. C2×#103 | D101 | semidirect |
| 134. #103 | C2×D101 | semidirect |
| 213. C2 | #20265538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| C2×#15692244 | 2 |
| #20265538 | 2 |
| C2×#15692179 | 2 |
| C2×#15692177 | 2 |
| C2×#15692175 | 2 |
| C2×#15692165 | 2 |
| C2×#103×C101 | 2 |
| C2×#489 | 101 |