Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20273538 | C2 | semidirect |
| 3. #20272681 | C2 | semidirect |
| 4. #20272635 | C2 | semidirect |
| 5. C53×#1368 | C2 | semidirect |
| 19. D848 | C8 | semidirect |
| 39. D424 | C2×C8 | semidirect |
| 42. C16×C53 | C2×C8 | semidirect |
| 68. #1368 | D53 | semidirect |
| 84. C53 | #12067 | semidirect |
| 112. C16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276592 | 2 |
| #20273538 | 2 |
| #20272681 | 2 |
| #20272635 | 2 |
| C53×#1368 | 2 |
| #12067 | 53 |