Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20287347 | C2 | semidirect |
| 2. #20286380 | C2 | semidirect |
| 3. #20274177 | C2 | semidirect |
| 4. #20274156 | C2 | semidirect |
| 5. #20273961 | C2 | semidirect |
| 6. #20273777 | C2 | semidirect |
| 7. #20273601 | C2 | semidirect |
| 8. C8×Dic212 | C2 | semidirect |
| 9. C53×#1706 | C2 | semidirect |
| 123. Dic212 | D8 | semidirect |
| 179. #1706 | D53 | semidirect |
| 220. C53 | #19888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287347 | 2 |
| #20286380 | 2 |
| #20274177 | 2 |
| #20274156 | 2 |
| #20273961 | 2 |
| #20273777 | 2 |
| #20273601 | 2 |
| C8×Dic212 | 2 |
| C53×#1706 | 2 |
| #19888 | 53 |