Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261838 | C2 | semidirect |
| 2. C4⋊#13095523 | C2 | semidirect |
| 5. #20261829 | C2 | semidirect |
| 6. C4×#13095523 | C2 | semidirect |
| 67. C97 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261838 | 2 |
| C4⋊#13095523 | 2 |
| #20261832 | 2 |
| #20261829 | 2 |
| C4×#13095523 | 2 |
| #20261700 | 2 |
| #2164 | 97 |