Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 3. #20275696 | C2 | semidirect |
| 5. #20273280 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1274 | C2 | semidirect |
| 11. #16810996 | C4 | semidirect |
| 12. #16810970 | C4 | semidirect |
| 33. #13133217 | C2×C4 | semidirect |
| 34. #13133217 | C2×C4 | semidirect |
| 64. C4×C8×C53 | C2×C4 | semidirect |
| 96. C42×C53 | SD16 | semidirect |
| 195. #1274 | D53 | semidirect |
| 221. C53 | #9295 | semidirect |
| 257. C4×C8 | C4×D53 | semidirect |
| 308. C42 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285658 | 2 |
| #20277440 | 2 |
| #20275696 | 2 |
| #20273382 | 2 |
| #20273280 | 2 |
| #20272574 | 2 |
| C53×#1274 | 2 |
| #9295 | 53 |