Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20260859 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 5. #20260467 | C2 | semidirect |
| 6. C8×#11715895 | C2 | semidirect |
| 24. #13095499 | C8 | semidirect |
| 53. Dic194 | C2×C8 | semidirect |
| 59. #11715895 | C2×C8 | semidirect |
| 60. #11715895 | SD16 | semidirect |
| 78. C97 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260859 | 2 |
| C4×#13095499 | 2 |
| D4×#11715895 | 2 |
| #20260485 | 2 |
| #20260467 | 2 |
| C8×#11715895 | 2 |
| D4⋊C8×C97 | 2 |
| C8×SD16 | 97 |