Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2190 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 360 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 |
|---|---|---|
| 1. C22×#13133274 | C2 | semidirect |
| 2. C22×(C2×#6157)⋊C4 | C2 | semidirect |
| 3. C2×#16811474 | C2 | direct (N × H) |
| 8. C2×#13133274 | C22 | semidirect |
| 10. C2×(C2×#6157)⋊C4 | C22 | semidirect |
| 11. #16811474 | C22 | direct (N × H) |
| 16. C2×#13133188 | C4 | semidirect |
| 18. C22×C4⋊Dic53 | C4 | semidirect |
| 20. C23×D4×C53 | C4 | semidirect |
| 28. #13133274 | C23 | semidirect |
| 30. (C2×#6157)⋊C4 | C23 | semidirect |
| 46. #13133188 | C2×C4 | semidirect |
| 49. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 55. C22×D4×C53 | C2×C4 | semidirect |
| 76. C2×D4×C53 | C22×C4 | semidirect |
| 104. C4⋊Dic53 | C22×C4 | semidirect |
| 155. C22×C53 | #327 | semidirect |
| 181. C2×C53 | C2×#327 | semidirect |
| 189. C23×D4 | #6157 | semidirect |
| 204. C53 | C22×#327 | semidirect |
| 213. C22×D4 | C2×#6157 | semidirect |
| 260. C2×D4 | C22×#6157 | semidirect |
| 348. C22 | #16811474 | direct (N × H) |
| 363. C2 | C2×#16811474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133274 | 2 |
| C22×(C2×#6157)⋊C4 | 2 |
| C2×#16811474 | 2 |
| C22×#13133188 | 2 |
| C22×#327 | 53 |