Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
840 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20273230 | C2 | semidirect |
| 3. #20273042 | C2 | semidirect |
| 4. #20272601 | C2 | semidirect |
| 5. C53×#2273 | C2 | semidirect |
| 10. #16810559 | C4 | semidirect |
| 11. #16810532 | C4 | semidirect |
| 21. C22×D212 | C2×C4 | semidirect |
| 29. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 38. #13133124 | C2×C4 | semidirect |
| 53. #95×C53 | D4 | semidirect |
| 182. #2273 | D53 | semidirect |
| 209. C53 | #9409 | semidirect |
| 242. #95 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279646 | 2 |
| #20273230 | 2 |
| #20273042 | 2 |
| #20272601 | 2 |
| C53×#2273 | 2 |
| #9409 | 53 |