Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20261684 | C2 | semidirect |
| 3. #20261680 | C2 | semidirect |
| 4. C4⋊C4×#87604 | C2 | semidirect |
| 6. C42×#87604 | C2 | semidirect |
| 18. #15690805 | C4 | semidirect |
| 19. #15690804 | C4 | semidirect |
| 20. #15690803 | C4 | semidirect |
| 24. #126×C97 | C4 | semidirect |
| 38. C4⋊Dic97 | C2×C4 | semidirect |
| 39. #13095490 | C2×C4 | semidirect |
| 40. #13095490 | C2×C4 | semidirect |
| 44. C4×Dic97 | C2×C4 | semidirect |
| 45. C4⋊C4×C97 | C2×C4 | semidirect |
| 47. C42×C97 | C2×C4 | semidirect |
| 80. #87604 | #126 | direct (N × H) |
| 91. C97 | C4×#126 | semidirect |
| 103. #126 | #87604 | direct (N × H) |
| 128. C4⋊C4 | C2×#87604 | semidirect |
| 138. C42 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261685 | 2 |
| #20261684 | 2 |
| #20261680 | 2 |
| C4⋊C4×#87604 | 2 |
| C22⋊C4×#87604 | 2 |
| C42×#87604 | 2 |
| #126×D97 | 2 |
| C4×#126 | 97 |