Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16810985 | C2 | semidirect |
| 3. #20274019 | C2 | direct (N × H) |
| 4. C2×#16810363 | C2 | semidirect |
| 5. C2×#16810362 | C2 | semidirect |
| 6. C2×C53×#497 | C2 | semidirect |
| 16. #16810985 | C22 | semidirect |
| 19. C2×#13133128 | C22 | semidirect |
| 20. #16810363 | C22 | semidirect |
| 21. #16810362 | C22 | semidirect |
| 24. C2×C4⋊Q8×C53 | C22 | semidirect |
| 27. C53×#497 | C22 | semidirect |
| 28. C2×#97×C53 | C22 | semidirect |
| 55. #13133128 | C23 | semidirect |
| 66. C4⋊Q8×C53 | C23 | semidirect |
| 74. #97×C53 | C23 | semidirect |
| 183. C2×#497 | D53 | semidirect |
| 189. C2×C53 | #1659 | semidirect |
| 198. C2×C4⋊Q8 | C2×D53 | semidirect |
| 206. #497 | C2×D53 | semidirect |
| 212. C2×#97 | C2×D53 | semidirect |
| 215. C53 | C2×#1659 | semidirect |
| 232. C4⋊Q8 | C22×D53 | semidirect |
| 261. #97 | C22×D53 | semidirect |
| 370. C2 | #20274019 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811365 | 2 |
| C2×#16810985 | 2 |
| #20274019 | 2 |
| C2×#16810363 | 2 |
| C2×#16810362 | 2 |
| C2×C53×#497 | 2 |
| C2×#1659 | 53 |