Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 8. #15692309 | C4 | semidirect |
| 9. C8×#87938 | C4 | semidirect |
| 13. #15692166 | C4 | semidirect |
| 14. #15692165 | C4 | semidirect |
| 15. C8×Dic101 | C4 | semidirect |
| 16. C4×C8×C101 | C4 | semidirect |
| 62. C101 | #1747 | semidirect |
| 78. C4×C8 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266140 | 2 |
| #20266046 | 2 |
| #20266045 | 2 |
| #20266044 | 2 |
| #20265131 | 2 |
| #1747 | 101 |