Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20284719 | C2 | semidirect |
| 3. #20275513 | C2 | semidirect |
| 4. #20273118 | C2 | semidirect |
| 5. #20273114 | C2 | semidirect |
| 6. #20272546 | C2 | semidirect |
| 7. C53×#3135 | C2 | semidirect |
| 200. #3135 | 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 |
|---|---|
| #20284719 | 2 |
| #20284711 | 2 |
| #20275513 | 2 |
| #20273118 | 2 |
| #20273114 | 2 |
| #20272546 | 2 |
| C53×#3135 | 2 |
| #10033 | 53 |