Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692300 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. C2×#15692251 | C2 | semidirect |
| 4. #20265347 | C2 | direct (N × H) |
| 5. C2×#15692181 | C2 | semidirect |
| 6. C2×#100×C101 | C2 | semidirect |
| 9. #15692300 | C22 | semidirect |
| 12. C22×D404 | C22 | semidirect |
| 17. #15692283 | C22 | semidirect |
| 21. #15692251 | C22 | semidirect |
| 22. C2×C4×Dic101 | C22 | semidirect |
| 23. #15692181 | C22 | semidirect |
| 25. C2×M16×C101 | C22 | semidirect |
| 26. #100×C101 | C22 | semidirect |
| 31. #13108074 | D4 | semidirect |
| 35. C2×Dic202 | D4 | semidirect |
| 39. C2×D404 | D4 | semidirect |
| 40. C2×D404 | C23 | semidirect |
| 55. C4×Dic101 | C23 | semidirect |
| 63. M16×C101 | C23 | semidirect |
| 94. D404 | C2×D4 | semidirect |
| 98. Dic202 | C2×D4 | semidirect |
| 122. C2×C101 | #453 | semidirect |
| 127. C101 | C2×#453 | semidirect |
| 133. C2×#100 | D101 | semidirect |
| 148. C2×M16 | C2×D101 | semidirect |
| 153. #100 | C2×D101 | semidirect |
| 188. M16 | C22×D101 | semidirect |
| 251. C2 | #20265347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692300 | 2 |
| C2×#15692283 | 2 |
| C2×#15692251 | 2 |
| #20265347 | 2 |
| C2×#15692181 | 2 |
| C2×#100×C101 | 2 |
| C2×#453 | 101 |