Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 277 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. C22×C4×Dic97 | C2 | semidirect |
| 3. #20260640 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260612 | C2 | semidirect |
| 6. C4×#13095488 | C2 | semidirect |
| 7. C2×#117×C97 | C2 | semidirect |
| 10. C2×#13095511 | C4 | semidirect |
| 30. C2×Dic194 | C2×C4 | semidirect |
| 33. C2×D388 | C2×C4 | semidirect |
| 43. C2×C4×D97 | C2×C4 | semidirect |
| 68. C2×C4×C97 | C22⋊C4 | semidirect |
| 82. C2×Dic97 | #41 | semidirect |
| 110. C97 | #2297 | semidirect |
| 112. C2×#117 | D97 | semidirect |
| 189. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C22×C4×Dic97 | 2 |
| #20260640 | 2 |
| #20260636 | 2 |
| #20260612 | 2 |
| C4×#13095488 | 2 |
| C2×#117×C97 | 2 |
| #2297 | 97 |