Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. C4×#13095495 | C2 | semidirect |
| 3. #20260465 | C2 | semidirect |
| 4. #20260462 | C2 | semidirect |
| 5. C2×C4⋊C8×C97 | C2 | semidirect |
| 95. C97 | #1483 | semidirect |
| 97. C2×C4⋊C8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261269 | 2 |
| C4×#13095495 | 2 |
| #20260465 | 2 |
| #20260462 | 2 |
| C2×C4⋊C8×C97 | 2 |
| #1483 | 97 |