Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20276319 | C2 | semidirect |
| 5. #20272802 | C2 | semidirect |
| 6. #20272797 | C2 | semidirect |
| 7. C53×#2150 | C2 | semidirect |
| 138. #2150 | D53 | semidirect |
| 165. C53 | #13129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276342 | 2 |
| #20276335 | 2 |
| #20276319 | 2 |
| #20274552 | 2 |
| #20272802 | 2 |
| #20272797 | 2 |
| C53×#2150 | 2 |
| #13129 | 53 |