Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
114 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 31 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. #20260517 | C2 | semidirect |
| 3. H(3,ℤ/4)×C97 | C2 | semidirect |
| 4. C2×D776 | C4 | semidirect |
| 7. #15690742 | C4 | semidirect |
| 53. C97 | #1339 | semidirect |
| 56. H(3,ℤ/4) | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260988 | 2 |
| #20260517 | 2 |
| H(3,ℤ/4)×C97 | 2 |
| #1339 | 97 |