Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
808 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×C53⋊#564 | C2 | semidirect |
| 4. #20274044 | C2 | semidirect |
| 5. #20274018 | C2 | semidirect |
| 6. #20273318 | C2 | semidirect |
| 7. C53×#1534 | C2 | semidirect |
| 148. #1534 | D53 | semidirect |
| 176. C53 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53⋊#564 | 2 |
| #20285907 | 2 |
| #20285118 | 2 |
| #20274044 | 2 |
| #20274018 | 2 |
| #20273318 | 2 |
| C53×#1534 | 2 |
| #19003 | 53 |