Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #20266201 | C2 | semidirect |
| 2. #20266200 | C2 | semidirect |
| 3. #20266196 | C2 | semidirect |
| 4. #20266184 | C2 | semidirect |
| 7. #20266142 | C2 | semidirect |
| 11. #15692322 | C22 | semidirect |
| 12. C4⋊#11717581 | C22 | semidirect |
| 18. #15692310 | C22 | semidirect |
| 19. C4×#11717581 | C22 | semidirect |
| 111. C101 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266201 | 2 |
| #20266200 | 2 |
| #20266196 | 2 |
| #20266184 | 2 |
| #20266148 | 2 |
| D101⋊(C22⋊C8) | 2 |
| #20266142 | 2 |
| #117×D101 | 2 |
| #2924 | 101 |