Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261290 | C2 | semidirect |
| 3. #20261108 | C2 | semidirect |
| 4. #20261087 | C2 | semidirect |
| 5. #20261083 | C2 | semidirect |
| 6. #20260965 | C2 | semidirect |
| 7. #20260822 | C2 | semidirect |
| 8. C4×C8×D97 | C2 | semidirect |
| 9. #498×C97 | C2 | semidirect |
| 87. C4×D97 | SD16 | semidirect |
| 89. C8×C97 | #41 | semidirect |
| 113. C97 | #3167 | semidirect |
| 116. #498 | D97 | semidirect |
| 203. C8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| #20261286 | 2 |
| #20261108 | 2 |
| #20261087 | 2 |
| #20261083 | 2 |
| #20260965 | 2 |
| #20260822 | 2 |
| C4×C8×D97 | 2 |
| #498×C97 | 2 |
| #3167 | 97 |