Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13108062 | C2 | semidirect |
| 2. C23×#11717579 | C2 | semidirect |
| 3. C2×#15692234 | C2 | semidirect |
| 4. #20265404 | C2 | direct (N × H) |
| 5. C2×#15692186 | C2 | semidirect |
| 6. C2×#15692178 | C2 | semidirect |
| 7. C2×#15692176 | C2 | semidirect |
| 11. C2×#13108062 | C22 | semidirect |
| 15. C22×#11717579 | C22 | semidirect |
| 17. #15692234 | C22 | semidirect |
| 21. #15692186 | C22 | semidirect |
| 22. #15692178 | C22 | semidirect |
| 23. #15692176 | C22 | semidirect |
| 40. C2×#11717579 | D4 | semidirect |
| 71. C23×C101 | SD16 | semidirect |
| 97. #11717579 | C2×D4 | semidirect |
| 107. C22×C101 | C2×SD16 | semidirect |
| 119. C2×C101 | #465 | semidirect |
| 124. C101 | C2×#465 | semidirect |
| 195. C23 | #13108062 | semidirect |
| 231. C22 | C2×#13108062 | semidirect |
| 243. C2 | #20265404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C23×#11717579 | 2 |
| C2×#15692234 | 2 |
| #20265404 | 2 |
| C2×#15692186 | 2 |
| C2×#15692178 | 2 |
| C2×#15692176 | 2 |
| C2×#121×C101 | 2 |
| C2×#465 | 101 |