Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1846 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1846 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 |
|---|---|---|
| 3. C2×#16811477 | C2 | direct (N × H) |
| 11. #16811477 | C22 | direct (N × H) |
| 15. C2×#13133193 | C4 | semidirect |
| 17. C22×C4⋊Dic53 | C4 | semidirect |
| 20. C23×Q8×C53 | C4 | semidirect |
| 42. #13133193 | C2×C4 | semidirect |
| 45. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 52. C22×Q8×C53 | C2×C4 | semidirect |
| 70. C2×Q8×C53 | C22×C4 | semidirect |
| 95. C4⋊Dic53 | C22×C4 | semidirect |
| 138. C22×C53 | #328 | semidirect |
| 164. C2×C53 | C2×#328 | semidirect |
| 171. C23×Q8 | #6157 | semidirect |
| 187. C53 | C22×#328 | semidirect |
| 191. C22×Q8 | C2×#6157 | semidirect |
| 232. C2×Q8 | C22×#6157 | semidirect |
| 314. C22 | #16811477 | direct (N × H) |
| 329. C2 | C2×#16811477 | 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×#16811477 | 2 |
| C22×#13133193 | 2 |
| C22×#328 | 53 |