Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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×#15690769 | C2 | semidirect |
| 3. #20260596 | C2 | semidirect |
| 4. #20260592 | C2 | semidirect |
| 6. C4×#13095488 | C2 | semidirect |
| 7. C2×#117×C97 | C2 | semidirect |
| 12. C22×C4×D97 | C4 | semidirect |
| 16. C2×C4⋊Dic97 | C22 | semidirect |
| 19. C2×C4×Dic97 | C22 | semidirect |
| 20. #15690717 | C22 | semidirect |
| 23. C2×C4⋊C4×C97 | C22 | semidirect |
| 25. C2×C42×C97 | C22 | semidirect |
| 73. C2×C4×C97 | C22⋊C4 | semidirect |
| 101. C2×D97 | #117 | semidirect |
| 114. C97 | #2280 | semidirect |
| 117. C2×#117 | D97 | semidirect |
| 133. C2×C4⋊C4 | C2×D97 | semidirect |
| 138. C2×C42 | C2×D97 | semidirect |
| 195. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D97 | 2 |
| C2×#15690769 | 2 |
| #20260596 | 2 |
| #20260592 | 2 |
| #20260590 | 2 |
| C4×#13095488 | 2 |
| C2×#117×C97 | 2 |
| #2280 | 97 |