Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C2×#16811063 | C2 | semidirect |
| 2. #20285210 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276436 | C2 | semidirect |
| 5. #20275614 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 244. C53 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| #20285210 | 2 |
| #20276451 | 2 |
| #20276436 | 2 |
| #20275614 | 2 |
| #20272800 | 2 |
| C53×#3414 | 2 |
| #13335 | 53 |