Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20274887 | C2 | semidirect |
| 3. #20273503 | C2 | semidirect |
| 6. #20272605 | C2 | semidirect |
| 7. C53×#1278 | C2 | semidirect |
| 126. D212 | #108 | semidirect |
| 169. #1278 | D53 | semidirect |
| 196. C53 | #8898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283836 | 2 |
| #20274887 | 2 |
| #20273503 | 2 |
| #20273155 | 2 |
| #20273098 | 2 |
| #20272605 | 2 |
| C53×#1278 | 2 |
| #8898 | 53 |