Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276465 | C2 | semidirect |
| 3. #20276464 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20275469 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 74. #106×C53 | D4 | semidirect |
| 190. #2145 | D53 | semidirect |
| 220. C53 | #13416 | semidirect |
| 263. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285158 | 2 |
| #20276465 | 2 |
| #20276464 | 2 |
| #20276450 | 2 |
| #20275469 | 2 |
| #20272794 | 2 |
| C53×#2145 | 2 |
| #13416 | 53 |