Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#15692309 | C2 | semidirect |
| 4. C2×C8×#87938 | C2 | semidirect |
| 5. (C2×#87938)⋊C8 | C2 | semidirect |
| 6. (C2×#87938)⋊C8 | C2 | semidirect |
| 16. #15692312 | C4 | semidirect |
| 17. C22⋊#11717581 | C4 | semidirect |
| 23. C22⋊#11717579 | C4 | semidirect |
| 24. #15692167 | C4 | semidirect |
| 25. #15692167 | C4 | semidirect |
| 26. C22⋊C8×C101 | C4 | semidirect |
| 126. C101 | #1750 | semidirect |
| 150. C22⋊C8 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692334 | 2 |
| D101⋊(C22⋊C8) | 2 |
| C2×#15692309 | 2 |
| C2×C8×#87938 | 2 |
| (C2×#87938)⋊C8 | 2 |
| C22⋊C8×D101 | 2 |
| #1750 | 101 |