Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 126 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×C4⋊#11715897 | C2 | semidirect |
| 3. #20261601 | C2 | semidirect |
| 30. C2×C4×D97 | C8 | semidirect |
| 85. C2×D97 | C4⋊C8 | semidirect |
| 88. C4×C97 | C22⋊C8 | semidirect |
| 102. C97 | #1797 | semidirect |
| 194. C4 | #15690867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715897 | 2 |
| C2×#15690867 | 2 |
| #20261601 | 2 |
| C2×C42×D97 | 2 |
| #1797 | 97 |