Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20272785 | C2 | semidirect |
| 5. #20272784 | C2 | semidirect |
| 6. #20272778 | C2 | semidirect |
| 7. C53×#1367 | C2 | semidirect |
| 112. #1367 | D53 | semidirect |
| 132. C53 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276517 | 2 |
| C4⋊C16×D53 | 2 |
| C8×#11719912 | 2 |
| #20272785 | 2 |
| #20272784 | 2 |
| #20272778 | 2 |
| C53×#1367 | 2 |
| #12016 | 53 |