Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265805 | C2 | semidirect |
| 3. #20265542 | C2 | semidirect |
| 4. #20265537 | C2 | semidirect |
| 5. #20265532 | C2 | semidirect |
| 6. #20265524 | C2 | semidirect |
| 7. #20265183 | C2 | semidirect |
| 8. #20265179 | C2 | semidirect |
| 9. #20265174 | C2 | semidirect |
| 10. C2×#15692177 | C2 | semidirect |
| 11. #405×C101 | C2 | semidirect |
| 14. #15692255 | C22 | semidirect |
| 17. #15692247 | C22 | semidirect |
| 26. #15692180 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 33. #15692177 | C22 | semidirect |
| 34. #15692177 | C22 | semidirect |
| 35. #15692177 | C22 | semidirect |
| 39. #97×C101 | C22 | semidirect |
| 40. C4×C8×C101 | C22 | semidirect |
| 136. C101 | #3136 | semidirect |
| 147. #405 | D101 | semidirect |
| 175. #97 | C2×D101 | semidirect |
| 176. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265805 | 2 |
| #20265746 | 2 |
| #20265542 | 2 |
| #20265537 | 2 |
| #20265532 | 2 |
| #20265524 | 2 |
| #20265183 | 2 |
| #20265179 | 2 |
| #20265174 | 2 |
| C2×#15692177 | 2 |
| #405×C101 | 2 |
| #3136 | 101 |