Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20291025 | C2 | semidirect |
| 4. #20290863 | C2 | semidirect |
| 5. #20289787 | C2 | semidirect |
| 6. #20289761 | C2 | semidirect |
| 24. #16811066 | C4 | semidirect |
| 26. #16811064 | C4 | semidirect |
| 27. #16811063 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 62. C2×Dic212 | C2×C4 | semidirect |
| 78. #13133157 | C2×C4 | semidirect |
| 82. C2×Q16×C53 | C2×C4 | semidirect |
| 85. M32×C53 | C2×C4 | semidirect |
| 230. #510 | #6157 | semidirect |
| 247. C53 | #13026 | semidirect |
| 263. C2×Q16 | C2×#6157 | semidirect |
| 288. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291469 | 2 |
| D53⋊#360 | 2 |
| #20291025 | 2 |
| #20290863 | 2 |
| #20289787 | 2 |
| #20289761 | 2 |
| #510×D53 | 2 |
| #13026 | 53 |