Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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. #15692310 | C4 | semidirect |
| 11. #15692309 | C4 | semidirect |
| 12. C8×#87938 | C4 | semidirect |
| 15. #15692166 | C4 | semidirect |
| 16. #15692165 | C4 | semidirect |
| 17. #97×C101 | C4 | semidirect |
| 47. #11717581 | C42 | semidirect |
| 48. C8×C101 | C42 | semidirect |
| 49. #11717579 | C42 | semidirect |
| 55. #87938 | #97 | direct (N × H) |
| 65. C101 | C4×#97 | semidirect |
| 81. #97 | #87938 | direct (N × H) |
| 114. C8 | C4×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266136 | 2 |
| C2×#15692309 | 2 |
| C2×C8×#87938 | 2 |
| C42×#87938 | 2 |
| #97×D101 | 2 |
| C4×#97 | 101 |