Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. C2×#15692309 | C2 | semidirect |
| 3. C2×C8×#87938 | C2 | semidirect |
| 5. (C2×#87938)⋊C8 | C2 | semidirect |
| 6. (C2×#87938)⋊C8 | C2 | semidirect |
| 13. #15692312 | C4 | semidirect |
| 14. C22⋊#11717581 | C4 | semidirect |
| 19. C2×#13108058 | C4 | semidirect |
| 20. C2×#13108057 | C4 | semidirect |
| 21. C2×#13108057 | C4 | semidirect |
| 26. C2×M16×C101 | C4 | semidirect |
| 75. C2×#87938 | M16 | semidirect |
| 97. C8×C101 | C22⋊C4 | semidirect |
| 99. #11717579 | C22⋊C4 | semidirect |
| 129. C101 | #1753 | semidirect |
| 143. C2×M16 | #87938 | semidirect |
| 228. C8 | C22⋊#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊(C22⋊C8) | 2 |
| C2×#15692309 | 2 |
| C2×C8×#87938 | 2 |
| C4×C22⋊#87938 | 2 |
| (C2×#87938)⋊C8 | 2 |
| C2×M16×D101 | 2 |
| #1753 | 101 |