Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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×C4×#11715895 | C2 | semidirect |
| 4. #20260490 | C2 | semidirect |
| 7. C22×#11715895 | C4 | semidirect |
| 11. C22⋊#11715895 | C4 | semidirect |
| 33. C22⋊C4×C97 | C8 | semidirect |
| 48. C2×C4×C97 | C2×C8 | semidirect |
| 55. #11715895 | C22⋊C4 | direct (N × H) |
| 59. C22×C97 | C4×C8 | semidirect |
| 75. C97 | C8×C22⋊C4 | semidirect |
| 108. C22⋊C4 | #11715895 | direct (N × H) |
| 123. C2×C4 | C2×#11715895 | semidirect |
| 134. C22 | C4×#11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715895 | 2 |
| C2×C22⋊#11715895 | 2 |
| C2×C4×#11715895 | 2 |
| #20260490 | 2 |
| C4×C22⋊C4×C97 | 2 |
| C8×C22⋊C4 | 97 |