Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 4. #20260656 | C2 | direct (N × H) |
| 31. C22×Dic97 | Q8 | semidirect |
| 42. C22×C4×C97 | Q8 | semidirect |
| 57. C2×C4×C97 | C2×Q8 | semidirect |
| 68. C2×Dic97 | C2×Q8 | semidirect |
| 85. C2×C97 | #395 | semidirect |
| 92. C97 | C2×#395 | semidirect |
| 131. C22×C4 | Dic194 | semidirect |
| 161. C2×C4 | C2×Dic194 | semidirect |
| 177. C2 | #20260656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic194 | 2 |
| C22×C4⋊Dic97 | 2 |
| C22×#13095490 | 2 |
| #20260656 | 2 |
| C2×#15690717 | 2 |
| C2×#95×C97 | 2 |
| C2×#395 | 97 |