Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. C4×#13095521 | C2 | semidirect |
| 3. C42×#87604 | C2 | semidirect |
| 4. #20261605 | C2 | semidirect |
| 10. #15690874 | C4 | direct (N × H) |
| 14. C4×Dic194 | C4 | semidirect |
| 15. #15690775 | C4 | semidirect |
| 16. D4×Dic97 | C4 | semidirect |
| 23. C4×D4×C97 | C4 | semidirect |
| 26. #13095521 | C2×C4 | semidirect |
| 31. C4×#87604 | C2×C4 | semidirect |
| 63. D4×C97 | C42 | semidirect |
| 82. Dic194 | C42 | semidirect |
| 94. C4×C97 | #104 | semidirect |
| 100. Dic97 | #104 | semidirect |
| 108. C97 | C4×#104 | semidirect |
| 121. C4×D4 | #87604 | semidirect |
| 171. D4 | C4×#87604 | semidirect |
| 207. C4 | #15690874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690874 | 2 |
| C4×#13095521 | 2 |
| C42×#87604 | 2 |
| #20261605 | 2 |
| C4×#13095510 | 2 |
| C4×#104 | 97 |