Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×C22⋊#87604 | C2 | semidirect |
| 2. C2×#15690869 | C2 | direct (N × H) |
| 6. C2×C22⋊#87604 | C22 | semidirect |
| 7. #15690869 | C22 | direct (N × H) |
| 8. C24×D97 | C4 | semidirect |
| 12. C22×D388 | C4 | semidirect |
| 14. C23×C4×C97 | C4 | semidirect |
| 18. C22⋊#87604 | C23 | semidirect |
| 24. C23×D97 | C2×C4 | semidirect |
| 32. C2×D388 | C2×C4 | semidirect |
| 37. C22×C4×C97 | C2×C4 | semidirect |
| 54. C22×D97 | C22×C4 | semidirect |
| 62. C2×C4×C97 | C22×C4 | semidirect |
| 67. C22×C97 | #99 | semidirect |
| 87. C2×C97 | C2×#99 | semidirect |
| 93. C97 | C22×#99 | semidirect |
| 104. C23×C4 | #87604 | semidirect |
| 128. C22×C4 | C2×#87604 | semidirect |
| 157. C2×C4 | C22×#87604 | semidirect |
| 172. C22 | #15690869 | direct (N × H) |
| 183. C2 | C2×#15690869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#87604 | 2 |
| C2×#15690869 | 2 |
| C23×D388 | 2 |
| C22×#99 | 97 |