Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20260814 | C2 | semidirect |
| 3. #20260486 | C2 | semidirect |
| 4. #20260464 | C2 | semidirect |
| 5. #322×C97 | C2 | semidirect |
| 40. C8×C97 | M16 | semidirect |
| 56. C97 | #1594 | semidirect |
| 61. #322 | D97 | semidirect |
| 97. C8 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D776 | 2 |
| #20260814 | 2 |
| #20260486 | 2 |
| #20260464 | 2 |
| #322×C97 | 2 |
| #1594 | 97 |