Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #20260486 | C2 | semidirect |
| 5. #20260484 | C2 | semidirect |
| 6. #20260481 | C2 | semidirect |
| 7. #498×C97 | C2 | semidirect |
| 56. C8×C97 | SD16 | semidirect |
| 77. C97 | #1671 | semidirect |
| 78. #498 | D97 | semidirect |
| 136. C8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261022 | 2 |
| #20260937 | 2 |
| C8×D388 | 2 |
| #20260486 | 2 |
| #20260484 | 2 |
| #20260481 | 2 |
| #498×C97 | 2 |
| #1671 | 97 |