Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15690745 | C2 | semidirect |
| 3. C2×#15690738 | C2 | semidirect |
| 4. #20260703 | C2 | semidirect |
| 5. #20260702 | C2 | semidirect |
| 6. C2×C4×#11715895 | C2 | semidirect |
| 7. C2×#104×C97 | C2 | semidirect |
| 11. C2×#13095501 | C4 | semidirect |
| 12. C2×#13095499 | C4 | semidirect |
| 13. C2×#13095498 | C4 | semidirect |
| 14. C2×#13095496 | C4 | semidirect |
| 120. C97 | #1974 | semidirect |
| 124. C2×#104 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| C2×#15690745 | 2 |
| C2×#15690738 | 2 |
| #20260703 | 2 |
| #20260702 | 2 |
| C2×C4×#11715895 | 2 |
| C2×#104×C97 | 2 |
| #1974 | 97 |