Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#15692302 | C2 | semidirect |
| 2. C22×#13108062 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265319 | C2 | semidirect |
| 5. #20265314 | C2 | semidirect |
| 6. #20265187 | C2 | semidirect |
| 7. #20265173 | C2 | semidirect |
| 8. #20265145 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 15. C2×#13108073 | C22 | semidirect |
| 18. C2×Q8×D101 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 28. #15692179 | C22 | semidirect |
| 29. #15692176 | C22 | semidirect |
| 30. #15692167 | C22 | semidirect |
| 48. C2×Dic202 | D4 | semidirect |
| 69. #41×C101 | D4 | semidirect |
| 146. C101 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 191. #41 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C22×#13108062 | 2 |
| #20265744 | 2 |
| #20265319 | 2 |
| #20265314 | 2 |
| #20265187 | 2 |
| #20265173 | 2 |
| #20265145 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3010 | 101 |