Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
888 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 365 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 |
|---|---|---|
| 3. #20260605 | C2 | semidirect |
| 4. #20260604 | C2 | semidirect |
| 5. #384×C97 | C2 | semidirect |
| 12. C42×D97 | C4 | semidirect |
| 24. C4×Dic97 | C2×C4 | semidirect |
| 28. C42×C97 | C2×C4 | semidirect |
| 42. C4×D97 | C4⋊C4 | semidirect |
| 50. C4×C97 | C2×C4⋊C4 | semidirect |
| 52. Dic97 | C2×C4⋊C4 | semidirect |
| 56. D97 | #384 | direct (N × H) |
| 58. C97 | C2×#384 | semidirect |
| 63. #384 | D97 | direct (N × H) |
| 86. C42 | C4×D97 | semidirect |
| 110. C4 | C4⋊C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D97 | 2 |
| C2×C42×D97 | 2 |
| #20260605 | 2 |
| #20260604 | 2 |
| #384×C97 | 2 |
| C2×#384 | 97 |