Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20261133 | C2 | semidirect |
| 3. #20261108 | C2 | semidirect |
| 4. #20261082 | C2 | semidirect |
| 5. #322×C97 | C2 | semidirect |
| 38. C8×C97 | SD16 | semidirect |
| 52. C97 | #1715 | semidirect |
| 57. #322 | D97 | semidirect |
| 90. C8 | #13095500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261133 | 2 |
| #20261112 | 2 |
| #20261108 | 2 |
| #20261082 | 2 |
| #322×C97 | 2 |
| #1715 | 97 |