Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #20276968 | C2 | semidirect |
| 3. #20276766 | C2 | semidirect |
| 5. #20272765 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 96. D4×C53 | Q32 | semidirect |
| 163. C53 | #12322 | semidirect |
| 242. D4 | Dic424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic212 | 2 |
| #20276968 | 2 |
| #20276766 | 2 |
| #20274080 | 2 |
| #20272765 | 2 |
| #20272680 | 2 |
| C53×D4⋊C16 | 2 |
| #12322 | 53 |