Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
994 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 169 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. #336×D53 | C2 | semidirect |
| 3. #20272536 | C2 | semidirect |
| 4. #20272535 | C2 | semidirect |
| 5. C53×#1270 | C2 | semidirect |
| 15. #16810378 | C22 | semidirect |
| 18. C53×#336 | C22 | semidirect |
| 25. C2×D4×D53 | C8 | semidirect |
| 60. C2×D4×C53 | C2×C8 | semidirect |
| 75. C2×D212 | C2×C8 | semidirect |
| 190. #1270 | D53 | direct (N × H) |
| 198. D53 | #1270 | direct (N × H) |
| 211. #336 | C2×D53 | semidirect |
| 212. C53 | C2×#1270 | semidirect |
| 263. C2×D4 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #390×D53 | 2 |
| #336×D53 | 2 |
| #20272536 | 2 |
| #20272535 | 2 |
| C53×#1270 | 2 |
| C2×#1270 | 53 |