Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20260504 | C2 | semidirect |
| 6. #15690727 | C4 | direct (N × H) |
| 17. #13095495 | C2×C4 | semidirect |
| 67. C4×C97 | #100 | semidirect |
| 76. C97 | C4×#100 | semidirect |
| 143. C4 | #15690727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690727 | 2 |
| C4×#13095495 | 2 |
| #20260504 | 2 |
| C2×C4×D4×C97 | 2 |
| C4×#100 | 97 |