Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. C2×#15692324 | C2 | semidirect |
| 2. C2×#15692318 | C2 | semidirect |
| 4. C2×#15692309 | C2 | semidirect |
| 5. (C2×#87938)⋊Q8 | C2 | semidirect |
| 20. C2×#13108063 | C4 | semidirect |
| 21. C2×#13108062 | C4 | semidirect |
| 22. C2×#13108061 | C4 | semidirect |
| 26. C2×SD16×C101 | C4 | semidirect |
| 102. C8×C101 | C22⋊C4 | semidirect |
| 103. #11717579 | C22⋊C4 | semidirect |
| 133. C101 | #1973 | semidirect |
| 148. C2×SD16 | #87938 | semidirect |
| 236. C8 | C22⋊#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×#15692318 | 2 |
| C2×#15692317 | 2 |
| C2×#15692309 | 2 |
| (C2×#87938)⋊Q8 | 2 |
| #20266129 | 2 |
| C2×SD16×D101 | 2 |
| #1973 | 101 |