Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
436 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. C2×C4×#11715895 | C2 | semidirect |
| 3. #20260490 | C2 | semidirect |
| 6. C22⋊#11715895 | C4 | direct (N × H) |
| 16. C2×#11715895 | C2×C4 | semidirect |
| 22. C22×C4×C97 | C8 | semidirect |
| 56. C22×C97 | C4×C8 | semidirect |
| 64. C4×C97 | C22⋊C8 | semidirect |
| 73. C97 | C4×C22⋊C8 | semidirect |
| 92. C22×C4 | #11715895 | semidirect |
| 129. C22 | C4×#11715895 | semidirect |
| 137. C4 | C22⋊#11715895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715895 | 2 |
| C2×C4×#11715895 | 2 |
| #20260490 | 2 |
| C22×C42×C97 | 2 |
| C4×C22⋊C8 | 97 |