Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13108075 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. C2×#15692226 | C2 | semidirect |
| 4. #20265321 | C2 | direct (N × H) |
| 5. C2×#15692179 | C2 | semidirect |
| 6. C2×#15692177 | C2 | semidirect |
| 7. C2×#15692167 | C2 | semidirect |
| 8. C22×SD16×C101 | C2 | semidirect |
| 12. C2×#13108075 | C22 | semidirect |
| 19. C2×#13108059 | C22 | semidirect |
| 22. #15692226 | C22 | semidirect |
| 25. #15692179 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 27. #15692167 | C22 | semidirect |
| 31. C2×SD16×C101 | C22 | semidirect |
| 42. C2×D404 | D4 | semidirect |
| 63. C2×Q8×C101 | D4 | semidirect |
| 89. Q8×C101 | C2×D4 | semidirect |
| 107. D404 | C2×D4 | semidirect |
| 137. C2×C101 | #449 | semidirect |
| 144. C101 | C2×#449 | semidirect |
| 146. C22×SD16 | D101 | semidirect |
| 165. C2×SD16 | C2×D101 | semidirect |
| 185. C2×Q8 | C22⋊D101 | semidirect |
| 233. Q8 | C2×C22⋊D101 | semidirect |
| 283. C2 | #20265321 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108075 | 2 |
| C22×#13108059 | 2 |
| C2×#15692226 | 2 |
| #20265321 | 2 |
| C2×#15692179 | 2 |
| C2×#15692177 | 2 |
| C2×#15692167 | 2 |
| C22×SD16×C101 | 2 |
| C2×#449 | 101 |