Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20277543 | C2 | semidirect |
| 3. #20274660 | C2 | semidirect |
| 4. #20273231 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272601 | C2 | semidirect |
| 7. C53×#1964 | C2 | semidirect |
| 9. C2×#13133243 | C4 | semidirect |
| 15. #16810622 | C4 | semidirect |
| 43. C2×#11719917 | C2×C4 | semidirect |
| 60. C22×D4×C53 | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 188. D212 | #99 | semidirect |
| 232. #1964 | D53 | semidirect |
| 267. C53 | #9365 | semidirect |
| 277. C22×D4 | C4×D53 | semidirect |
| 292. C2×C4⋊C4 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283965 | 2 |
| #20277543 | 2 |
| #20274660 | 2 |
| #20273231 | 2 |
| #20272621 | 2 |
| #20272601 | 2 |
| C53×#1964 | 2 |
| #9365 | 53 |