Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265540 | C2 | semidirect |
| 4. #20265538 | C2 | semidirect |
| 5. #20265533 | C2 | semidirect |
| 6. #20265522 | C2 | semidirect |
| 7. #20265181 | C2 | semidirect |
| 8. #20265178 | C2 | semidirect |
| 9. C2×#15692177 | C2 | semidirect |
| 10. #20265132 | C2 | semidirect |
| 11. #416×C101 | C2 | semidirect |
| 15. #15692254 | C22 | semidirect |
| 18. #15692246 | C22 | semidirect |
| 26. #15692179 | C22 | semidirect |
| 29. #15692176 | C22 | semidirect |
| 32. #15692165 | C22 | semidirect |
| 33. C8×Dic101 | C22 | semidirect |
| 37. #103×C101 | C22 | semidirect |
| 38. #103×C101 | C22 | semidirect |
| 39. #102×C101 | C22 | semidirect |
| 40. #102×C101 | C22 | semidirect |
| 136. C101 | #3136 | semidirect |
| 145. #416 | D101 | semidirect |
| 166. #103 | C2×D101 | semidirect |
| 167. #103 | C2×D101 | semidirect |
| 173. #102 | C2×D101 | semidirect |
| 174. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265805 | 2 |
| #20265741 | 2 |
| #20265540 | 2 |
| #20265538 | 2 |
| #20265533 | 2 |
| #20265522 | 2 |
| #20265181 | 2 |
| #20265178 | 2 |
| C2×#15692177 | 2 |
| #20265132 | 2 |
| #416×C101 | 2 |
| #3136 | 101 |