Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 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 |
|---|---|---|
| 1. #20283743 | C2 | semidirect |
| 3. #20273428 | C2 | semidirect |
| 4. #20273428 | C2 | semidirect |
| 5. #20273055 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 56. C4⋊#88322 | D4 | semidirect |
| 67. C4⋊C8×C53 | D4 | semidirect |
| 220. #1285 | D53 | semidirect |
| 250. C53 | #9457 | semidirect |
| 283. C4⋊C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283743 | 2 |
| #20279657 | 2 |
| #20273428 | 2 |
| #20273055 | 2 |
| #20272571 | 2 |
| C53×#1285 | 2 |
| #9457 | 53 |