Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #20275503 | C2 | semidirect |
| 5. #20272813 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 7. C2×C53×#365 | C2 | semidirect |
| 20. #16810431 | C4 | semidirect |
| 46. #13133153 | C2×C4 | semidirect |
| 57. C2×C16×C53 | C2×C4 | semidirect |
| 148. C2×#365 | D53 | semidirect |
| 177. C53 | #12949 | semidirect |
| 202. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283598 | 2 |
| #20276462 | 2 |
| #20276444 | 2 |
| #20275503 | 2 |
| #20272813 | 2 |
| #20272800 | 2 |
| C2×C53×#365 | 2 |
| #12949 | 53 |