Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
720 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 720 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 |
|---|---|---|
| 2. #20273433 | C2 | semidirect |
| 3. #20273431 | C2 | semidirect |
| 4. #20273339 | C2 | semidirect |
| 5. #20273047 | C2 | semidirect |
| 6. #20273047 | C2 | semidirect |
| 7. C53×#1533 | C2 | semidirect |
| 232. #1533 | D53 | semidirect |
| 268. C53 | #8523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811242 | 2 |
| #20273433 | 2 |
| #20273431 | 2 |
| #20273339 | 2 |
| #20273047 | 2 |
| C53×#1533 | 2 |
| #8523 | 53 |