Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 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. C22×#13095488 | C2 | semidirect |
| 4. #20260637 | C2 | direct (N × H) |
| 5. C22×C42×C97 | C2 | semidirect |
| 9. C22×D388 | C4 | semidirect |
| 13. C2×C4⋊Dic97 | C22 | semidirect |
| 15. C2×#13095488 | C22 | semidirect |
| 19. C2×C42×C97 | C22 | semidirect |
| 29. C2×D388 | C2×C4 | semidirect |
| 41. C22×C4×C97 | D4 | semidirect |
| 64. C2×C4×C97 | C22⋊C4 | semidirect |
| 68. C2×C4×C97 | C2×D4 | semidirect |
| 90. C4×C97 | C2×C22⋊C4 | semidirect |
| 92. C2×C97 | #390 | semidirect |
| 100. C97 | C2×#390 | semidirect |
| 104. C22×C42 | D97 | semidirect |
| 119. C2×C42 | C2×D97 | semidirect |
| 138. C22×C4 | D388 | semidirect |
| 168. C2×C4 | #13095488 | semidirect |
| 172. C2×C4 | C2×D388 | semidirect |
| 191. C4 | C2×#13095488 | semidirect |
| 193. C2 | #20260637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C22×C4⋊Dic97 | 2 |
| C22×#13095488 | 2 |
| #20260637 | 2 |
| C22×C42×C97 | 2 |
| C2×#390 | 97 |