Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
592 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20272739 | C2 | semidirect |
| 4. #20272736 | C2 | semidirect |
| 12. C2×C22⋊Q8×C53 | C4 | semidirect |
| 14. C53×#399 | C4 | semidirect |
| 18. C53×#393 | C4 | semidirect |
| 21. C53×#380 | C4 | semidirect |
| 32. C22×Q8×C53 | C2×C4 | semidirect |
| 41. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 56. #95×C53 | C2×C4 | semidirect |
| 57. #95×C53 | C2×C4 | semidirect |
| 222. C2×C22⋊Q8 | Dic53 | semidirect |
| 226. #399 | Dic53 | semidirect |
| 230. #393 | Dic53 | semidirect |
| 233. #380 | Dic53 | semidirect |
| 239. C53 | #11716 | semidirect |
| 241. C22×Q8 | C2×Dic53 | semidirect |
| 252. C2×C4⋊C4 | C2×Dic53 | semidirect |
| 273. #95 | C2×Dic53 | semidirect |
| 274. #95 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810390 | 2 |
| C2×#16810347 | 2 |
| #20272739 | 2 |
| #20272736 | 2 |
| C53×#2626 | 2 |
| #11716 | 53 |