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. #20261640 | C2 | direct (N × H) |
| 6. #15690869 | C22 | semidirect |
| 8. C22×D388 | C4 | semidirect |
| 11. #15690807 | C4 | semidirect |
| 13. C2×C42×C97 | C4 | semidirect |
| 28. C2×D388 | C2×C4 | semidirect |
| 34. C42×C97 | C2×C4 | semidirect |
| 80. C2×C97 | #353 | semidirect |
| 86. C97 | C2×#353 | semidirect |
| 97. C2×C42 | #87604 | semidirect |
| 120. C42 | C2×#87604 | semidirect |
| 169. C2 | #20261640 | 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 |
| #20261640 | 2 |
| C2×#15690807 | 2 |
| C2×#353 | 97 |