Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 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 |
|---|---|---|
| 2. C22×C4⋊Dic97 | C2 | semidirect |
| 3. #20260737 | C2 | direct (N × H) |
| 4. C2×#15690735 | C2 | semidirect |
| 5. C2×#15690732 | C2 | semidirect |
| 6. C22×M16×C97 | C2 | semidirect |
| 9. C2×#13095511 | C4 | semidirect |
| 19. C2×C4⋊Dic97 | C22 | semidirect |
| 20. #15690735 | C22 | semidirect |
| 21. #15690732 | C22 | semidirect |
| 24. C2×M16×C97 | C22 | semidirect |
| 29. #13095511 | C2×C4 | semidirect |
| 32. C2×Dic194 | C2×C4 | semidirect |
| 36. C2×D388 | C2×C4 | semidirect |
| 85. D388 | C22×C4 | semidirect |
| 89. Dic194 | C22×C4 | semidirect |
| 110. C2×C97 | #417 | semidirect |
| 116. C97 | C2×#417 | semidirect |
| 118. C22×M16 | D97 | semidirect |
| 134. C2×M16 | C2×D97 | semidirect |
| 227. C2 | #20260737 | direct (N × H) |
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 |
| #20260737 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C22×M16×C97 | 2 |
| C2×#417 | 97 |