Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#15690832 | C2 | semidirect |
| 2. C2×#15690830 | C2 | semidirect |
| 3. #20261281 | C2 | semidirect |
| 4. #20261128 | C2 | semidirect |
| 5. #20261126 | C2 | semidirect |
| 6. #20261123 | C2 | semidirect |
| 7. #20261121 | C2 | semidirect |
| 8. C2×#15690720 | C2 | semidirect |
| 9. C2×#135×C97 | C2 | semidirect |
| 51. C2×#11715895 | D4 | semidirect |
| 68. C2×C8×C97 | D4 | semidirect |
| 117. C97 | #3150 | semidirect |
| 120. C2×#135 | D97 | semidirect |
| 180. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690830 | 2 |
| #20261281 | 2 |
| #20261128 | 2 |
| #20261126 | 2 |
| #20261123 | 2 |
| #20261121 | 2 |
| C2×#15690720 | 2 |
| C2×#135×C97 | 2 |
| #3150 | 97 |