Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 384 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. D4×Dic212 | C2 | semidirect |
| 2. #20276971 | C2 | semidirect |
| 3. #20276756 | C2 | semidirect |
| 5. #20272765 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 89. Dic212 | D8 | semidirect |
| 98. D4×C53 | SD32 | semidirect |
| 147. D4⋊C16 | D53 | semidirect |
| 170. C53 | #12318 | semidirect |
| 254. D4 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic212 | 2 |
| #20276971 | 2 |
| #20276756 | 2 |
| #20274070 | 2 |
| #20272765 | 2 |
| #20272680 | 2 |
| C53×D4⋊C16 | 2 |
| #12318 | 53 |