Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 1. #20291370 | C2 | semidirect |
| 2. #20291024 | C2 | semidirect |
| 3. C2×#16811535 | C2 | semidirect |
| 4. D53⋊#350 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289778 | C2 | semidirect |
| 25. #16810894 | C4 | semidirect |
| 26. #16810893 | C4 | semidirect |
| 29. #16810890 | C4 | semidirect |
| 32. C53×#472 | C4 | semidirect |
| 61. C2×D424 | C2×C4 | semidirect |
| 78. #13133153 | C2×C4 | semidirect |
| 84. C2×D8×C53 | C2×C4 | semidirect |
| 86. #108×C53 | C2×C4 | semidirect |
| 257. #472 | #6157 | semidirect |
| 271. C53 | #12996 | semidirect |
| 288. C2×D8 | C2×#6157 | semidirect |
| 315. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291370 | 2 |
| #20291024 | 2 |
| C2×#16811535 | 2 |
| D53⋊#350 | 2 |
| #20289791 | 2 |
| #20289778 | 2 |
| #472×D53 | 2 |
| #12996 | 53 |