Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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×#15690767 | C2 | semidirect |
| 4. #20260631 | C2 | semidirect |
| 5. #20260624 | C2 | semidirect |
| 6. C4×#13095488 | C2 | semidirect |
| 7. C42×Dic97 | C2 | semidirect |
| 8. C4×C4⋊C4×C97 | C2 | semidirect |
| 11. C4×D388 | C4 | semidirect |
| 44. C4×Dic97 | D4 | semidirect |
| 91. C4×C97 | #117 | semidirect |
| 103. C97 | #2293 | semidirect |
| 109. C4×C4⋊C4 | D97 | semidirect |
| 197. C4 | #15690767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C2×#15690767 | 2 |
| #20260636 | 2 |
| #20260631 | 2 |
| #20260624 | 2 |
| C4×#13095488 | 2 |
| C42×Dic97 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2293 | 97 |