Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×#15690865 | C2 | semidirect |
| 4. #20261601 | C2 | semidirect |
| 7. C2×#13095519 | C4 | semidirect |
| 11. #15690867 | C4 | semidirect |
| 61. #11715897 | C22⋊C4 | semidirect |
| 71. C2×D97 | #97 | semidirect |
| 85. C97 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C2×#15690867 | 2 |
| C2×#15690865 | 2 |
| #20261601 | 2 |
| #20260582 | 2 |
| #1752 | 97 |