Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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. #20260601 | C2 | direct (N × H) |
| 11. C2×C42×C97 | C4 | semidirect |
| 25. C42×C97 | C2×C4 | semidirect |
| 52. C2×C97 | #382 | semidirect |
| 58. C97 | C2×#382 | semidirect |
| 68. C2×C42 | Dic97 | semidirect |
| 83. C42 | C2×Dic97 | semidirect |
| 110. C2 | #20260601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic97 | 2 |
| #20260601 | 2 |
| C2×#15690717 | 2 |
| C22×C42×C97 | 2 |
| C2×#382 | 97 |