Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 5. C22×#11715895 | C4 | semidirect |
| 9. C22⋊#11715895 | C4 | semidirect |
| 28. C22⋊C4×C97 | C8 | semidirect |
| 78. C97 | #1282 | semidirect |
| 106. C22⋊C4 | #11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715895 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #1282 | 97 |