Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20265977 | C2 | semidirect |
| 2. C2×#15692277 | C2 | semidirect |
| 3. C2×#15692261 | C2 | semidirect |
| 4. #20265453 | C2 | semidirect |
| 5. #20265448 | C2 | semidirect |
| 6. #20265441 | C2 | semidirect |
| 7. #20265159 | C2 | semidirect |
| 8. C2×#108×C101 | C2 | semidirect |
| 20. C2×Dic404 | C22 | semidirect |
| 21. C2×#13108063 | C22 | semidirect |
| 22. C2×D808 | C22 | semidirect |
| 30. #15692173 | C22 | semidirect |
| 31. #15692171 | C22 | semidirect |
| 34. #108×C101 | C22 | semidirect |
| 35. #108×C101 | C22 | semidirect |
| 133. C101 | #3067 | semidirect |
| 140. C2×#108 | D101 | semidirect |
| 165. #108 | C2×D101 | semidirect |
| 166. #108 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692277 | 2 |
| C2×#15692261 | 2 |
| #20265453 | 2 |
| #20265448 | 2 |
| #20265441 | 2 |
| #20265159 | 2 |
| C2×#108×C101 | 2 |
| #3067 | 101 |