Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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. #20274333 | C2 | semidirect |
| 4. #20274332 | C2 | semidirect |
| 5. #20274331 | C2 | semidirect |
| 7. C53×#1713 | C2 | semidirect |
| 67. C8×D53 | Q16 | semidirect |
| 82. C8×C53 | C2×Q16 | semidirect |
| 84. #88322 | C2×Q16 | semidirect |
| 100. #1713 | D53 | direct (N × H) |
| 104. D53 | #1713 | direct (N × H) |
| 121. C53 | C2×#1713 | semidirect |
| 182. C8 | Q16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D53 | 2 |
| #494×D53 | 2 |
| #20274333 | 2 |
| #20274332 | 2 |
| #20274331 | 2 |
| C82×D53 | 2 |
| C53×#1713 | 2 |
| C2×#1713 | 53 |