Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20261153 | C2 | semidirect |
| 2. #20261152 | C2 | semidirect |
| 4. #20260555 | C2 | semidirect |
| 5. #20260518 | C2 | semidirect |
| 6. #20260510 | C2 | semidirect |
| 7. #350×C97 | C2 | semidirect |
| 72. C97 | #2171 | semidirect |
| 78. #350 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261153 | 2 |
| #20261152 | 2 |
| #20260850 | 2 |
| #20260555 | 2 |
| #20260518 | 2 |
| #20260510 | 2 |
| #350×C97 | 2 |
| #2171 | 97 |