Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20266126 | C2 | semidirect |
| 3. C4×C4⋊#87938 | C2 | semidirect |
| 5. #20266113 | C2 | semidirect |
| 6. C42×#87938 | C2 | semidirect |
| 17. #15692214 | C4 | semidirect |
| 18. #15692213 | C4 | semidirect |
| 19. #15692212 | C4 | semidirect |
| 20. #15692212 | C4 | semidirect |
| 21. #15692211 | C4 | semidirect |
| 26. #117×C101 | C4 | semidirect |
| 109. C101 | #2298 | semidirect |
| 123. #117 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266127 | 2 |
| #20266126 | 2 |
| C4×C4⋊#87938 | 2 |
| C4×C22⋊#87938 | 2 |
| #20266113 | 2 |
| C42×#87938 | 2 |
| #117×D101 | 2 |
| #2298 | 101 |