Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C2×#16811510 | C2 | semidirect |
| 4. #108×#6157 | C2 | semidirect |
| 5. #20289778 | C2 | semidirect |
| 6. #20289777 | C2 | semidirect |
| 18. #16811538 | C4 | semidirect |
| 19. #16811537 | C4 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 39. D53⋊C16 | C2×C4 | semidirect |
| 41. #13133288 | C2×C4 | semidirect |
| 62. C2×#11719908 | C2×C4 | semidirect |
| 65. #13133153 | C2×C4 | semidirect |
| 68. C2×C16×C53 | C2×C4 | semidirect |
| 69. #108×C53 | C2×C4 | semidirect |
| 205. #359 | #6157 | semidirect |
| 208. C53 | #12640 | semidirect |
| 236. C2×C16 | C2×#6157 | semidirect |
| 241. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×#6157 | 2 |
| D53⋊#359 | 2 |
| C2×#16811510 | 2 |
| #108×#6157 | 2 |
| #20289778 | 2 |
| #20289777 | 2 |
| #359×D53 | 2 |
| #12640 | 53 |