Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1170 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20285836 | C2 | semidirect |
| 3. #20273717 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. #20273039 | C2 | semidirect |
| 6. C53×#2546 | C2 | semidirect |
| 179. #2546 | D53 | semidirect |
| 211. C53 | #18408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20285836 | 2 |
| #20273717 | 2 |
| #20273209 | 2 |
| #20273039 | 2 |
| C53×#2546 | 2 |
| #18408 | 53 |