Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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. C22⋊C4×#87604 | C2 | semidirect |
| 4. #20261612 | C2 | semidirect |
| 6. C23×#87604 | C4 | semidirect |
| 10. C2×C4⋊#87604 | C4 | semidirect |
| 11. C2×C22⋊#87604 | C4 | semidirect |
| 15. C2×C4×#87604 | C4 | semidirect |
| 16. #15690869 | C4 | semidirect |
| 17. #15690868 | C4 | semidirect |
| 21. #15690725 | C4 | semidirect |
| 22. #15690724 | C4 | semidirect |
| 23. #99×C97 | C4 | semidirect |
| 39. C22⋊#87604 | C2×C4 | semidirect |
| 52. C22⋊Dic97 | C2×C4 | semidirect |
| 55. C22⋊C4×C97 | C2×C4 | semidirect |
| 56. C23×C97 | C42 | semidirect |
| 64. C22×D97 | C42 | semidirect |
| 87. C2×C4×C97 | C42 | semidirect |
| 91. C2×Dic97 | C42 | semidirect |
| 121. #87604 | #99 | direct (N × H) |
| 136. C97 | C4×#99 | semidirect |
| 158. #99 | #87604 | direct (N × H) |
| 188. C22⋊C4 | C2×#87604 | semidirect |
| 203. C23 | C4×#87604 | semidirect |
| 232. C2×C4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#87604 | 2 |
| D97⋊#99 | 2 |
| C22⋊C4×#87604 | 2 |
| #20261612 | 2 |
| #99×D97 | 2 |
| C4×#99 | 97 |