Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 94 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. #20290147 | C2 | semidirect |
| 3. #20290099 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289570 | C2 | semidirect |
| 26. #16810914 | C4 | semidirect |
| 27. #16810913 | C4 | semidirect |
| 28. #16810900 | C4 | semidirect |
| 32. C53×#474 | C4 | semidirect |
| 55. #13133217 | C2×C4 | semidirect |
| 73. C4⋊#88322 | C2×C4 | semidirect |
| 78. C4⋊Q8×C53 | C2×C4 | semidirect |
| 81. C4⋊C8×C53 | C2×C4 | semidirect |
| 241. #474 | #6157 | semidirect |
| 258. C53 | #9175 | semidirect |
| 264. C4⋊Q8 | C2×#6157 | semidirect |
| 295. C4⋊C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291228 | 2 |
| #20290147 | 2 |
| #20290099 | 2 |
| #20290015 | 2 |
| #20289611 | 2 |
| #20289570 | 2 |
| #20284507 | 2 |
| #9175 | 53 |