Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 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. #20260601 | C2 | semidirect |
| 4. #20260600 | C2 | semidirect |
| 5. #20260599 | C2 | semidirect |
| 7. #382×C97 | C2 | semidirect |
| 16. C42×D97 | C4 | semidirect |
| 35. C4×Dic97 | C2×C4 | semidirect |
| 36. C4×Dic97 | C2×C4 | semidirect |
| 41. C42×C97 | C2×C4 | semidirect |
| 82. D97 | #382 | direct (N × H) |
| 84. C97 | C2×#382 | semidirect |
| 90. #382 | D97 | direct (N × H) |
| 125. C42 | 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 |
| #20260601 | 2 |
| #20260600 | 2 |
| #20260599 | 2 |
| #95×D97 | 2 |
| #382×C97 | 2 |
| C2×#382 | 97 |