Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20272632 | C2 | semidirect |
| 4. #20272631 | C2 | semidirect |
| 5. C53×#1311 | C2 | semidirect |
| 19. C16×D53 | C8 | semidirect |
| 38. C16×C53 | C2×C8 | semidirect |
| 39. #11719908 | C2×C8 | semidirect |
| 63. #1311 | D53 | direct (N × H) |
| 66. D53 | #1311 | direct (N × H) |
| 76. C53 | C2×#1311 | semidirect |
| 101. C16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D53 | 2 |
| C82×D53 | 2 |
| #20272632 | 2 |
| #20272631 | 2 |
| C53×#1311 | 2 |
| C2×#1311 | 53 |