Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1126 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 3. #20273793 | C2 | direct (N × H) |
| 4. C2×#16810372 | C2 | semidirect |
| 5. C2×Q8⋊#88322 | C2 | semidirect |
| 6. C2×Q82×C53 | C2 | semidirect |
| 17. #16810372 | C22 | semidirect |
| 18. Q8⋊#88322 | C22 | semidirect |
| 21. Q82×C53 | C22 | semidirect |
| 73. C2×Q8×C53 | SD16 | semidirect |
| 116. Q8×C53 | C2×SD16 | semidirect |
| 152. C2×Q82 | D53 | semidirect |
| 158. C2×C53 | #1623 | semidirect |
| 166. Q82 | C2×D53 | semidirect |
| 182. C53 | C2×#1623 | semidirect |
| 229. C2×Q8 | #11719924 | semidirect |
| 272. Q8 | C2×#11719924 | semidirect |
| 308. C2 | #20273793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810997 | 2 |
| C2×#16810823 | 2 |
| #20273793 | 2 |
| C2×#16810372 | 2 |
| C2×Q8⋊#88322 | 2 |
| C2×Q82×C53 | 2 |
| C2×#1623 | 53 |