Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276901 | C2 | semidirect |
| 3. #20276896 | C2 | semidirect |
| 4. #20276155 | C2 | semidirect |
| 5. #20272731 | C2 | semidirect |
| 6. #20272731 | C2 | semidirect |
| 7. C53×#1315 | C2 | semidirect |
| 16. C2×#13133151 | C22 | semidirect |
| 23. #16810388 | C22 | semidirect |
| 25. C53×C22⋊C16 | C22 | semidirect |
| 26. C53×C22⋊C16 | C22 | semidirect |
| 163. #1315 | D53 | semidirect |
| 186. C22⋊C16 | C2×D53 | semidirect |
| 187. C22⋊C16 | C2×D53 | semidirect |
| 190. C53 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285580 | 2 |
| #20276901 | 2 |
| #20276896 | 2 |
| #20276155 | 2 |
| #20272731 | 2 |
| C53×#1315 | 2 |
| #12284 | 53 |