Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20265193 | C2 | semidirect |
| 3. #20265173 | C2 | semidirect |
| 4. #20265171 | C2 | semidirect |
| 5. #20265150 | C2 | semidirect |
| 6. #20265145 | C2 | semidirect |
| 7. #421×C101 | C2 | semidirect |
| 10. #15692302 | C4 | semidirect |
| 12. #15692301 | C4 | semidirect |
| 20. C22×#11717579 | C22 | semidirect |
| 21. #15692214 | C22 | semidirect |
| 30. C2×M16×C101 | C22 | semidirect |
| 31. #117×C101 | C22 | semidirect |
| 167. C101 | #1794 | semidirect |
| 170. #421 | D101 | semidirect |
| 188. C2×M16 | C2×D101 | semidirect |
| 191. #117 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| #20265193 | 2 |
| #20265173 | 2 |
| #20265171 | 2 |
| #20265150 | 2 |
| #20265145 | 2 |
| #421×C101 | 2 |
| #1794 | 101 |