Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13095499 | C2 | semidirect |
| 3. C2×#15690798 | C2 | semidirect |
| 4. #20260950 | C2 | direct (N × H) |
| 5. C2×C4⋊#11715895 | C2 | semidirect |
| 6. C2×#15690733 | C2 | semidirect |
| 7. C2×#15690730 | C2 | semidirect |
| 8. C2×C4×D4×C97 | C2 | semidirect |
| 12. C2×#13095499 | C22 | semidirect |
| 18. #15690798 | C22 | semidirect |
| 21. C4⋊#11715895 | C22 | semidirect |
| 22. #15690733 | C22 | semidirect |
| 23. #15690730 | C22 | semidirect |
| 27. C4×D4×C97 | C22 | semidirect |
| 118. C2×C97 | #463 | semidirect |
| 124. C97 | C2×#463 | semidirect |
| 128. C2×C4×D4 | D97 | semidirect |
| 146. C4×D4 | C2×D97 | semidirect |
| 243. C2 | #20260950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C22×#13095496 | 2 |
| C2×#15690798 | 2 |
| #20260950 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690733 | 2 |
| C2×#15690730 | 2 |
| C2×C4×D4×C97 | 2 |
| C2×#463 | 97 |