Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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×#15690884 | C2 | semidirect |
| 2. C22×#13095514 | C2 | semidirect |
| 3. C22⋊#13095514 | C2 | semidirect |
| 64. C97 | #2113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690884 | 2 |
| C22×#13095514 | 2 |
| C22⋊#13095514 | 2 |
| C2×#15690817 | 2 |
| #2113 | 97 |