Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#15690840 | C2 | semidirect |
| 3. C22×#13095500 | C2 | semidirect |
| 4. #20260998 | C2 | direct (N × H) |
| 5. C2×#15690746 | C2 | semidirect |
| 6. C2×#15690728 | C2 | semidirect |
| 7. C2×#15690726 | C2 | semidirect |
| 8. C2×#131×C97 | C2 | semidirect |
| 12. #15690840 | C22 | semidirect |
| 19. C2×#13095500 | C22 | semidirect |
| 25. #15690746 | C22 | semidirect |
| 26. #15690728 | C22 | semidirect |
| 27. #15690726 | C22 | semidirect |
| 30. #131×C97 | C22 | semidirect |
| 135. C2×C97 | #471 | semidirect |
| 139. C97 | C2×#471 | semidirect |
| 143. C2×#131 | D97 | semidirect |
| 164. #131 | C2×D97 | semidirect |
| 275. C2 | #20260998 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690835 | 2 |
| C22×#13095500 | 2 |
| #20260998 | 2 |
| C2×#15690746 | 2 |
| C2×#15690728 | 2 |
| C2×#15690726 | 2 |
| C2×#131×C97 | 2 |
| C2×#471 | 97 |