Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
428 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 10. #15690802 | C4 | semidirect |
| 99. C97 | #2336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690802 | 2 |
| #20260630 | 2 |
| #20260620 | 2 |
| #20260619 | 2 |
| #20260618 | 2 |
| #20260616 | 2 |
| #20260603 | 2 |
| C4×#13095490 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2336 | 97 |