Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #20265214 | C2 | direct (N × H) |
| 4. C2×#15692189 | C2 | semidirect |
| 5. C2×#15692186 | C2 | semidirect |
| 6. C2×#107×C101 | C2 | semidirect |
| 9. C2×C8×D101 | C4 | semidirect |
| 16. #15692189 | C22 | semidirect |
| 17. #15692186 | C22 | semidirect |
| 20. #107×C101 | C22 | semidirect |
| 30. C8×D101 | C2×C4 | semidirect |
| 75. C2×C101 | #427 | semidirect |
| 81. C101 | C2×#427 | semidirect |
| 86. C2×#107 | D101 | semidirect |
| 100. #107 | C2×D101 | semidirect |
| 157. C2 | #20265214 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D101 | 2 |
| C2×#15692213 | 2 |
| #20265214 | 2 |
| C2×#15692189 | 2 |
| C2×#15692186 | 2 |
| C2×#107×C101 | 2 |
| C2×#427 | 101 |