Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
| 2. C2×#15692281 | C2 | semidirect |
| 3. C2×#15692275 | C2 | semidirect |
| 4. C22×#13108062 | C2 | semidirect |
| 5. #20265753 | C2 | semidirect |
| 6. #20265572 | C2 | semidirect |
| 7. #20265564 | C2 | semidirect |
| 8. #20265559 | C2 | semidirect |
| 9. #20265549 | C2 | semidirect |
| 10. #20265133 | C2 | semidirect |
| 11. #535×C101 | C2 | semidirect |
| 17. C2×#13108064 | C22 | semidirect |
| 18. C2×#13108064 | C22 | semidirect |
| 23. C2×#13108062 | C22 | semidirect |
| 24. C2×#13108062 | C22 | semidirect |
| 25. C2×#13108061 | C22 | semidirect |
| 27. C2×#13108059 | C22 | semidirect |
| 30. #15692255 | C22 | semidirect |
| 31. #15692243 | C22 | semidirect |
| 34. #15692166 | C22 | semidirect |
| 35. C4×#11717579 | C22 | semidirect |
| 64. #13108058 | D4 | semidirect |
| 65. C2×#11717579 | D4 | semidirect |
| 149. C101 | #3154 | semidirect |
| 155. #535 | 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×#15692281 | 2 |
| C2×#15692275 | 2 |
| C22×#13108062 | 2 |
| #20265753 | 2 |
| #20265572 | 2 |
| #20265564 | 2 |
| #20265559 | 2 |
| #20265549 | 2 |
| #20265133 | 2 |
| #535×C101 | 2 |
| #3154 | 101 |