Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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. D53⋊#364 | C2 | semidirect |
| 2. #20289909 | C2 | semidirect |
| 3. #20289680 | C2 | semidirect |
| 4. #20289679 | C2 | semidirect |
| 9. #16811545 | C22 | semidirect |
| 11. #16811464 | C22 | semidirect |
| 30. #13133240 | C8 | semidirect |
| 34. #13133236 | C8 | semidirect |
| 35. Q16×D53 | C8 | semidirect |
| 37. D8×D53 | C8 | semidirect |
| 76. Q16×C53 | C2×C8 | semidirect |
| 78. D8×C53 | C2×C8 | semidirect |
| 96. Dic212 | C2×C8 | semidirect |
| 97. D424 | C2×C8 | semidirect |
| 177. D53 | #1336 | semidirect |
| 195. C53 | C2×#1336 | semidirect |
| 249. Q16 | D53⋊C8 | semidirect |
| 256. D8 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| #20289909 | 2 |
| #20289680 | 2 |
| #20289679 | 2 |
| #443×D53 | 2 |
| C2×#1336 | 53 |