Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #20261706 | C2 | semidirect |
| 2. C2×(C2×#87604)⋊C4 | C2 | semidirect |
| 3. #20261588 | C2 | semidirect |
| 4. #20261586 | C2 | semidirect |
| 12. C2×#13095510 | C4 | semidirect |
| 16. #15690789 | C4 | semidirect |
| 21. #15690768 | C4 | semidirect |
| 22. #121×C97 | C4 | semidirect |
| 31. C2×Dic194 | C2×C4 | semidirect |
| 42. C4⋊Dic97 | C2×C4 | semidirect |
| 50. C2×D4×C97 | C2×C4 | semidirect |
| 52. C4⋊C4×C97 | C2×C4 | semidirect |
| 120. C97 | #1504 | semidirect |
| 134. #121 | #87604 | semidirect |
| 149. C2×D4 | C2×#87604 | semidirect |
| 167. C4⋊C4 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261706 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #20261588 | 2 |
| #20261586 | 2 |
| #20261245 | 2 |
| #1504 | 97 |