Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 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. C2×#15692278 | C2 | semidirect |
| 2. C2×#15692276 | C2 | semidirect |
| 3. #20265728 | C2 | semidirect |
| 4. #20265726 | C2 | semidirect |
| 5. #20265570 | C2 | semidirect |
| 6. #20265569 | C2 | semidirect |
| 7. #20265567 | C2 | semidirect |
| 8. #20265566 | C2 | semidirect |
| 9. #20265563 | C2 | semidirect |
| 10. #97×D101 | C2 | semidirect |
| 11. #497×C101 | C2 | semidirect |
| 65. C8×D101 | D4 | semidirect |
| 134. C101 | #3150 | semidirect |
| 141. #497 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×#15692276 | 2 |
| #20265728 | 2 |
| #20265726 | 2 |
| #20265570 | 2 |
| #20265569 | 2 |
| #20265567 | 2 |
| #20265566 | 2 |
| #20265563 | 2 |
| #97×D101 | 2 |
| #497×C101 | 2 |
| #3150 | 101 |