Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×#15690869 | C2 | semidirect |
| 2. #20261639 | C2 | direct (N × H) |
| 6. #15690869 | C22 | semidirect |
| 10. #15690806 | C4 | semidirect |
| 12. C2×C4×Dic97 | C4 | semidirect |
| 13. C22×D4×C97 | C4 | semidirect |
| 28. C4×Dic97 | C2×C4 | semidirect |
| 33. C2×D4×C97 | C2×C4 | semidirect |
| 81. C2×C97 | #353 | semidirect |
| 86. C97 | C2×#353 | semidirect |
| 92. C22×D4 | #87604 | semidirect |
| 113. C2×D4 | C2×#87604 | semidirect |
| 169. C2 | #20261639 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690869 | 2 |
| #20261639 | 2 |
| C2×#15690806 | 2 |
| C2×#353 | 97 |