Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276513 | C2 | semidirect |
| 3. #20273460 | C2 | semidirect |
| 4. #20272768 | C2 | semidirect |
| 5. #20272766 | C2 | semidirect |
| 6. #20272758 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 150. #1360 | D53 | semidirect |
| 175. C53 | #11943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285282 | 2 |
| #20276513 | 2 |
| #20273460 | 2 |
| #20272768 | 2 |
| #20272766 | 2 |
| #20272758 | 2 |
| C53×#1360 | 2 |
| #11943 | 53 |