Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
644 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20290827 | C2 | semidirect |
| 4. #20290826 | C2 | semidirect |
| 5. #20289549 | C2 | semidirect |
| 6. #20289549 | C2 | semidirect |
| 25. #16810367 | C4 | semidirect |
| 26. #16810366 | C4 | semidirect |
| 27. #16810366 | C4 | semidirect |
| 28. C53×#331 | C4 | semidirect |
| 64. C4⋊#88322 | C2×C4 | semidirect |
| 65. C4⋊#88322 | C2×C4 | semidirect |
| 69. C4⋊C8×C53 | C2×C4 | semidirect |
| 70. C4⋊C8×C53 | C2×C4 | semidirect |
| 267. #331 | #6157 | semidirect |
| 268. C53 | #8921 | semidirect |
| 304. C4⋊C8 | C2×#6157 | semidirect |
| 305. C4⋊C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291245 | 2 |
| #20290843 | 2 |
| #20290827 | 2 |
| #20290826 | 2 |
| #20289549 | 2 |
| #331×D53 | 2 |
| #8921 | 53 |