Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20285061 | C2 | semidirect |
| 2. #20284723 | C2 | semidirect |
| 4. #20273117 | C2 | semidirect |
| 5. #20273113 | C2 | semidirect |
| 6. #20272546 | C2 | semidirect |
| 7. C53×#1955 | C2 | semidirect |
| 203. #1955 | D53 | semidirect |
| 238. C53 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285061 | 2 |
| #20284723 | 2 |
| #20284715 | 2 |
| #20273117 | 2 |
| #20273113 | 2 |
| #20272546 | 2 |
| C53×#1955 | 2 |
| #10033 | 53 |