Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 10. #15692324 | C4 | semidirect |
| 11. C8×#87938 | C4 | semidirect |
| 15. #15692189 | C4 | semidirect |
| 16. #15692188 | C4 | semidirect |
| 17. #107×C101 | C4 | semidirect |
| 59. C8×C101 | C42 | semidirect |
| 60. #11717579 | C42 | semidirect |
| 70. #87938 | #107 | direct (N × H) |
| 85. C101 | C4×#107 | semidirect |
| 100. #107 | #87938 | direct (N × H) |
| 145. C8 | C4×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692324 | 2 |
| C2×C8×#87938 | 2 |
| C4⋊C4×#87938 | 2 |
| #20266050 | 2 |
| #107×D101 | 2 |
| C4×#107 | 101 |