Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#13095499 | C2 | semidirect |
| 2. C2×C4×Dic194 | C2 | semidirect |
| 3. #20260932 | C2 | direct (N × H) |
| 4. C2×C4⋊#11715895 | C2 | semidirect |
| 5. C2×#15690731 | C2 | semidirect |
| 9. C2×#13095499 | C22 | semidirect |
| 12. C4×Dic194 | C22 | semidirect |
| 16. C4⋊#11715895 | C22 | semidirect |
| 17. #15690731 | C22 | semidirect |
| 26. C2×Dic194 | D4 | semidirect |
| 62. C2×C4×C97 | SD16 | semidirect |
| 75. Dic194 | C2×D4 | semidirect |
| 87. C4×C97 | C2×SD16 | semidirect |
| 93. C2×C97 | #460 | semidirect |
| 98. C97 | C2×#460 | semidirect |
| 167. C2×C4 | #13095499 | semidirect |
| 187. C4 | C2×#13095499 | semidirect |
| 191. C2 | #20260932 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C2×C4×Dic194 | 2 |
| #20260932 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690731 | 2 |
| C2×#127×C97 | 2 |
| C2×#460 | 97 |