Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 6. #15690881 | C4 | direct (N × H) |
| 53. C4×C97 | #108 | semidirect |
| 57. Dic97 | #108 | semidirect |
| 64. C97 | C4×#108 | semidirect |
| 120. C4 | #15690881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690881 | 2 |
| C4×#13095521 | 2 |
| #20261611 | 2 |
| C4×C8×D97 | 2 |
| C4×#108 | 97 |