Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 1. #20291469 | C2 | semidirect |
| 2. D53⋊#360 | C2 | semidirect |
| 3. #20291024 | C2 | semidirect |
| 4. #20290864 | C2 | semidirect |
| 5. #20289787 | C2 | semidirect |
| 6. #20289761 | C2 | semidirect |
| 24. #16811061 | C4 | semidirect |
| 26. #16811059 | C4 | semidirect |
| 27. #16811058 | C4 | semidirect |
| 32. C53×#509 | C4 | semidirect |
| 64. C2×D424 | C2×C4 | semidirect |
| 78. #13133157 | C2×C4 | semidirect |
| 82. C2×D8×C53 | C2×C4 | semidirect |
| 85. M32×C53 | C2×C4 | semidirect |
| 122. Q16×C53 | C22⋊C4 | semidirect |
| 126. D8×C53 | C22⋊C4 | semidirect |
| 135. Dic212 | C22⋊C4 | semidirect |
| 138. D424 | C22⋊C4 | semidirect |
| 240. #509 | #6157 | semidirect |
| 257. C53 | #13025 | semidirect |
| 275. C2×D8 | C2×#6157 | semidirect |
| 299. M32 | C2×#6157 | semidirect |
| 335. Q16 | C22⋊#6157 | semidirect |
| 348. D8 | C22⋊#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 |
| #20291024 | 2 |
| #20290864 | 2 |
| #20289787 | 2 |
| #20289761 | 2 |
| #509×D53 | 2 |
| #13025 | 53 |