Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283307 | C2 | semidirect |
| 3. C2×#16810433 | C2 | semidirect |
| 4. #20276344 | C2 | semidirect |
| 5. #20272831 | C2 | semidirect |
| 6. #20272814 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 12. #16810895 | C4 | semidirect |
| 13. #16810890 | C4 | semidirect |
| 53. #13133153 | C2×C4 | semidirect |
| 65. C2×Q16×C53 | C2×C4 | semidirect |
| 67. C2×D8×C53 | C2×C4 | semidirect |
| 190. #2145 | D53 | semidirect |
| 222. C53 | #13005 | semidirect |
| 234. C2×Q16 | C4×D53 | semidirect |
| 236. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284431 | 2 |
| #20283307 | 2 |
| C2×#16810433 | 2 |
| #20276344 | 2 |
| #20272831 | 2 |
| #20272814 | 2 |
| C53×#2145 | 2 |
| #13005 | 53 |