Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20276469 | C2 | semidirect |
| 3. #20273472 | C2 | semidirect |
| 4. #20272774 | C2 | semidirect |
| 5. #20272772 | C2 | semidirect |
| 6. #20272761 | C2 | semidirect |
| 7. C53×#1361 | C2 | semidirect |
| 138. #1361 | D53 | semidirect |
| 161. C53 | #11986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285292 | 2 |
| #20276469 | 2 |
| #20273472 | 2 |
| #20272774 | 2 |
| #20272772 | 2 |
| #20272761 | 2 |
| C53×#1361 | 2 |
| #11986 | 53 |