Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #20276434 | C2 | semidirect |
| 5. #20275628 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 13. C2×#13133162 | C4 | semidirect |
| 33. C2×Dic212 | C2×C4 | semidirect |
| 59. C2×C16×C53 | C2×C4 | semidirect |
| 161. #1382 | D53 | semidirect |
| 186. C53 | #13019 | semidirect |
| 215. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| #20283566 | 2 |
| C2×#16810435 | 2 |
| #20276434 | 2 |
| #20275628 | 2 |
| #20272803 | 2 |
| C53×#1382 | 2 |
| #13019 | 53 |