Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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×#15690864 | C2 | semidirect |
| 3. C2×C8×#87604 | C2 | semidirect |
| 5. #20261600 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 13. #15690867 | C4 | semidirect |
| 14. C22⋊#11715897 | C4 | semidirect |
| 19. C2×#13095495 | C4 | semidirect |
| 20. C2×#13095494 | C4 | semidirect |
| 21. C2×#13095494 | C4 | semidirect |
| 26. C2×M16×C97 | C4 | semidirect |
| 75. C2×#87604 | M16 | semidirect |
| 97. C8×C97 | C22⋊C4 | semidirect |
| 99. #11715895 | C22⋊C4 | semidirect |
| 129. C97 | #1753 | semidirect |
| 143. C2×M16 | #87604 | semidirect |
| 228. C8 | C22⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261703 | 2 |
| C2×#15690864 | 2 |
| C2×C8×#87604 | 2 |
| C4×C22⋊#87604 | 2 |
| #20261600 | 2 |
| C2×M16×D97 | 2 |
| #1753 | 97 |