Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 109 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. C4⋊C8×Dic53 | C2 | semidirect |
| 3. #20273490 | C2 | semidirect |
| 5. #20272612 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 21. C53×#332 | C4 | semidirect |
| 22. C53×#331 | C4 | semidirect |
| 175. #332 | Dic53 | semidirect |
| 176. #331 | Dic53 | semidirect |
| 178. C53 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275544 | 2 |
| C4⋊C8×Dic53 | 2 |
| #20273490 | 2 |
| #20273114 | 2 |
| #20272612 | 2 |
| #20272547 | 2 |
| C53×#1540 | 2 |
| #9577 | 53 |