Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #20265084 | C2 | semidirect |
| 3. #20265069 | C2 | semidirect |
| 4. #20265067 | C2 | semidirect |
| 6. C4×#13108051 | C2 | semidirect |
| 7. #20265024 | C2 | semidirect |
| 8. #20265022 | C2 | semidirect |
| 9. #391×C101 | C2 | semidirect |
| 12. #15692244 | C4 | semidirect |
| 46. #13108051 | C2×C4 | semidirect |
| 47. #13108051 | C2×C4 | semidirect |
| 51. C4×Dic101 | C2×C4 | semidirect |
| 54. C2×Q8×C101 | C2×C4 | semidirect |
| 124. C101 | #2372 | semidirect |
| 127. #391 | D101 | semidirect |
| 159. C2×Q8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692244 | 2 |
| #20265084 | 2 |
| #20265069 | 2 |
| #20265067 | 2 |
| #20265055 | 2 |
| C4×#13108051 | 2 |
| #20265024 | 2 |
| #20265022 | 2 |
| #391×C101 | 2 |
| #2372 | 101 |