Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 83 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. D8×#88322 | C2 | semidirect |
| 3. #20273509 | C2 | semidirect |
| 4. #20272788 | C2 | semidirect |
| 5. #20272677 | C2 | semidirect |
| 6. #20272631 | C2 | semidirect |
| 7. C53×#1331 | C2 | semidirect |
| 27. #13133158 | C8 | semidirect |
| 49. D8×C53 | C2×C8 | semidirect |
| 64. D424 | C2×C8 | semidirect |
| 68. #11719908 | C2×C8 | semidirect |
| 112. #1331 | D53 | semidirect |
| 134. C53 | #12045 | semidirect |
| 163. D8 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133158 | 2 |
| D8×#88322 | 2 |
| #20273509 | 2 |
| #20272788 | 2 |
| #20272677 | 2 |
| #20272631 | 2 |
| C53×#1331 | 2 |
| #12045 | 53 |