Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 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. C8×D388 | C2 | semidirect |
| 3. #20260488 | C2 | semidirect |
| 4. #20260464 | C2 | semidirect |
| 5. C82×C97 | C2 | semidirect |
| 18. D776 | C8 | direct (N × H) |
| 35. D388 | C2×C8 | semidirect |
| 41. C8×C97 | C2×C8 | semidirect |
| 42. C8×C97 | D8 | semidirect |
| 59. C97 | C8×D8 | semidirect |
| 64. C82 | D97 | semidirect |
| 101. C8 | C8×D97 | semidirect |
| 102. C8 | D776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D776 | 2 |
| C8×D388 | 2 |
| #20260488 | 2 |
| #20260464 | 2 |
| C82×C97 | 2 |
| C8×D8 | 97 |