Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 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×#15692287 | C2 | semidirect |
| 3. C2×Q16×D101 | C2 | semidirect |
| 4. #20265752 | C2 | semidirect |
| 5. #20265570 | C2 | semidirect |
| 6. #20265569 | C2 | semidirect |
| 7. #20265562 | C2 | semidirect |
| 8. #20265561 | C2 | semidirect |
| 9. #20265555 | C2 | semidirect |
| 10. #20265131 | C2 | semidirect |
| 11. #494×C101 | C2 | semidirect |
| 122. C101 | #3156 | semidirect |
| 132. #494 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692287 | 2 |
| C2×#15692278 | 2 |
| C2×Q16×D101 | 2 |
| #20265752 | 2 |
| #20265570 | 2 |
| #20265569 | 2 |
| #20265562 | 2 |
| #20265561 | 2 |
| #20265555 | 2 |
| #20265131 | 2 |
| #494×C101 | 2 |
| #3156 | 101 |