Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 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. #20261102 | C2 | semidirect |
| 4. #20261087 | C2 | semidirect |
| 5. #20261086 | C2 | semidirect |
| 6. #20261085 | C2 | semidirect |
| 9. #487×C97 | C2 | semidirect |
| 107. C97 | #3139 | semidirect |
| 114. #487 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4⋊Q8×D97 | 2 |
| #20261102 | 2 |
| #20261087 | 2 |
| #20261086 | 2 |
| #20261085 | 2 |
| #20260742 | 2 |
| C4×#13095494 | 2 |
| #487×C97 | 2 |
| #3139 | 97 |