Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692285 | C2 | semidirect |
| 3. C2×#15692243 | C2 | semidirect |
| 4. #20265399 | C2 | semidirect |
| 5. #20265392 | C2 | semidirect |
| 6. #20265201 | C2 | semidirect |
| 7. #20265185 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. C4×#41×C101 | C2 | semidirect |
| 14. C2×#13108064 | C22 | semidirect |
| 15. C2×#13108062 | C22 | semidirect |
| 24. C4⋊#11717579 | C22 | semidirect |
| 25. #15692178 | C22 | semidirect |
| 28. C4×Q8×C101 | C22 | semidirect |
| 30. C4×D4×C101 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 130. C4×#41 | D101 | semidirect |
| 150. C4×Q8 | C2×D101 | semidirect |
| 152. C4×D4 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| C2×#15692280 | 2 |
| C2×#15692243 | 2 |
| #20265399 | 2 |
| #20265392 | 2 |
| #20265201 | 2 |
| #20265185 | 2 |
| #20265181 | 2 |
| C4×#41×C101 | 2 |
| #3040 | 101 |