Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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. #20285293 | C2 | semidirect |
| 2. #20285144 | C2 | semidirect |
| 3. #20285142 | C2 | semidirect |
| 4. #20274331 | C2 | semidirect |
| 5. #20274329 | C2 | semidirect |
| 6. #20274321 | C2 | semidirect |
| 7. #20274306 | C2 | semidirect |
| 8. C82×D53 | C2 | semidirect |
| 9. C53×#1709 | C2 | semidirect |
| 99. C8×D53 | D8 | semidirect |
| 124. #88322 | #135 | semidirect |
| 145. #1709 | D53 | semidirect |
| 176. C53 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285293 | 2 |
| #20285144 | 2 |
| #20285142 | 2 |
| #20274331 | 2 |
| #20274329 | 2 |
| #20274321 | 2 |
| #20274306 | 2 |
| C82×D53 | 2 |
| C53×#1709 | 2 |
| #19603 | 53 |