Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276526 | C2 | semidirect |
| 3. #20273019 | C2 | semidirect |
| 4. #20272692 | C2 | semidirect |
| 5. #20272688 | C2 | semidirect |
| 6. #20272687 | C2 | semidirect |
| 7. C53×#1336 | C2 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 23. C8×#88322 | C22 | semidirect |
| 25. C53×#364 | C22 | semidirect |
| 26. C53×#322 | C22 | semidirect |
| 76. Q16×C53 | M16 | semidirect |
| 78. D8×C53 | M16 | semidirect |
| 98. Dic212 | M16 | semidirect |
| 99. D424 | M16 | semidirect |
| 166. #1336 | D53 | semidirect |
| 187. #364 | C2×D53 | semidirect |
| 191. #322 | C2×D53 | semidirect |
| 193. C53 | #11669 | semidirect |
| 245. Q16 | #11719912 | semidirect |
| 252. D8 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283620 | 2 |
| #20276526 | 2 |
| #20273019 | 2 |
| #20272692 | 2 |
| #20272688 | 2 |
| #20272687 | 2 |
| C53×#1336 | 2 |
| #11669 | 53 |