Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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 |
|---|---|---|
| 2. C22×Q8×D101 | C2 | semidirect |
| 3. C2×#15692284 | C2 | direct (N × H) |
| 4. C22×Dic404 | C2 | semidirect |
| 5. C22×#13108064 | C2 | semidirect |
| 6. C22×#13108062 | C2 | semidirect |
| 7. C22×#13108057 | C2 | semidirect |
| 8. C22×SD16×C101 | C2 | semidirect |
| 15. C2×Q8×D101 | C22 | semidirect |
| 20. #15692284 | C22 | direct (N × H) |
| 21. C2×Dic404 | C22 | semidirect |
| 22. C2×#13108064 | C22 | semidirect |
| 23. C2×#13108062 | C22 | semidirect |
| 24. C2×#13108057 | C22 | semidirect |
| 28. C2×SD16×C101 | C22 | semidirect |
| 39. Q8×D101 | C23 | semidirect |
| 48. Dic404 | C23 | semidirect |
| 49. #13108064 | C23 | semidirect |
| 50. #13108062 | C23 | semidirect |
| 51. #13108057 | C23 | semidirect |
| 60. SD16×C101 | C23 | semidirect |
| 91. C22×C101 | #137 | semidirect |
| 102. C2×C101 | C2×#137 | semidirect |
| 106. C101 | C22×#137 | semidirect |
| 113. C22×SD16 | D101 | semidirect |
| 132. C2×SD16 | C2×D101 | semidirect |
| 164. SD16 | C22×D101 | semidirect |
| 199. C22 | #15692284 | direct (N × H) |
| 209. C2 | C2×#15692284 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C22×Q8×D101 | 2 |
| C2×#15692284 | 2 |
| C22×Dic404 | 2 |
| C22×#13108064 | 2 |
| C22×#13108062 | 2 |
| C22×#13108057 | 2 |
| C22×SD16×C101 | 2 |
| C22×#137 | 101 |