Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #20291025 | C2 | semidirect |
| 3. C2×#16811536 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289778 | C2 | semidirect |
| 25. #16810899 | C4 | semidirect |
| 26. #16810898 | C4 | semidirect |
| 29. #16810895 | C4 | semidirect |
| 32. C53×#473 | C4 | semidirect |
| 60. C2×Dic212 | C2×C4 | semidirect |
| 78. #13133153 | C2×C4 | semidirect |
| 84. C2×Q16×C53 | C2×C4 | semidirect |
| 86. #108×C53 | C2×C4 | semidirect |
| 248. #473 | #6157 | semidirect |
| 262. C53 | #12997 | semidirect |
| 278. C2×Q16 | C2×#6157 | semidirect |
| 306. #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 |
| #20291025 | 2 |
| C2×#16811536 | 2 |
| D53⋊#350 | 2 |
| #20289791 | 2 |
| #20289778 | 2 |
| #473×D53 | 2 |
| #12997 | 53 |