Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 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 |
|---|---|---|
| 2. C2×#15690808 | C2 | semidirect |
| 4. #20260938 | C2 | direct (N × H) |
| 5. C2×#15690739 | C2 | semidirect |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#15690734 | C2 | semidirect |
| 15. #15690808 | C22 | semidirect |
| 23. #15690739 | C22 | semidirect |
| 24. #15690735 | C22 | semidirect |
| 25. #15690734 | C22 | semidirect |
| 88. C2×Dic97 | SD16 | semidirect |
| 111. Dic97 | C2×SD16 | semidirect |
| 113. C2×C97 | #461 | semidirect |
| 118. C97 | C2×#461 | semidirect |
| 231. C2 | #20260938 | 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 |
| C2×#15690808 | 2 |
| C2×D4×Dic97 | 2 |
| #20260938 | 2 |
| C2×#15690739 | 2 |
| C2×#15690735 | 2 |
| C2×#15690734 | 2 |
| C22×SD16×C97 | 2 |
| C2×#461 | 97 |