Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20261105 | C2 | semidirect |
| 4. #20261104 | C2 | semidirect |
| 5. #20261103 | C2 | semidirect |
| 6. #20261102 | C2 | semidirect |
| 9. #491×C97 | C2 | semidirect |
| 86. D97 | #491 | direct (N × H) |
| 88. C97 | C2×#491 | semidirect |
| 95. #491 | D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D97 | 2 |
| #125×D97 | 2 |
| #20261105 | 2 |
| #20261104 | 2 |
| #20261103 | 2 |
| #20261102 | 2 |
| #103×D97 | 2 |
| #97×D97 | 2 |
| #491×C97 | 2 |
| C2×#491 | 97 |