Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692284 | C2 | semidirect |
| 2. C2×#15692279 | C2 | semidirect |
| 3. #20265725 | C2 | semidirect |
| 4. #124×D101 | C2 | semidirect |
| 5. #20265572 | C2 | semidirect |
| 6. #20265571 | C2 | semidirect |
| 7. #20265564 | C2 | semidirect |
| 8. #20265560 | C2 | semidirect |
| 9. #20265558 | C2 | semidirect |
| 10. #20265129 | C2 | semidirect |
| 11. #496×C101 | C2 | semidirect |
| 17. C2×Dic404 | C22 | semidirect |
| 18. C2×#13108064 | C22 | semidirect |
| 21. C2×#13108062 | C22 | semidirect |
| 24. #15692255 | C22 | semidirect |
| 28. #15692242 | C22 | semidirect |
| 34. #15692166 | C22 | semidirect |
| 35. C8×Dic101 | C22 | semidirect |
| 36. C2×SD16×C101 | C22 | semidirect |
| 38. #127×C101 | C22 | semidirect |
| 40. #97×C101 | C22 | semidirect |
| 62. #13108057 | D4 | semidirect |
| 135. C101 | #3153 | semidirect |
| 143. #496 | D101 | semidirect |
| 157. C2×SD16 | C2×D101 | semidirect |
| 162. #127 | C2×D101 | semidirect |
| 174. #97 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692284 | 2 |
| C2×#15692279 | 2 |
| #20265725 | 2 |
| #124×D101 | 2 |
| #20265572 | 2 |
| #20265571 | 2 |
| #20265564 | 2 |
| #20265560 | 2 |
| #20265558 | 2 |
| #20265129 | 2 |
| #496×C101 | 2 |
| #3153 | 101 |