Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20261588 | C2 | direct (N × H) |
| 11. C22×Dic194 | C4 | semidirect |
| 15. #15690790 | C4 | semidirect |
| 19. C2×C4⋊C4×C97 | C4 | semidirect |
| 29. C2×Dic194 | C2×C4 | semidirect |
| 44. C4⋊C4×C97 | C2×C4 | semidirect |
| 93. C2×C97 | #328 | semidirect |
| 101. C97 | C2×#328 | semidirect |
| 115. C2×C4⋊C4 | #87604 | semidirect |
| 143. C4⋊C4 | C2×#87604 | semidirect |
| 197. C2 | #20261588 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690867 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #20261588 | 2 |
| C2×#15690790 | 2 |
| C2×#328 | 97 |