Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277530 | C2 | semidirect |
| 2. #20275635 | C2 | semidirect |
| 3. #20273313 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 25. C53×#496 | C4 | semidirect |
| 26. C53×#489 | C4 | semidirect |
| 60. C4⋊Q8×C53 | C2×C4 | semidirect |
| 61. #127×C53 | C2×C4 | semidirect |
| 78. #97×C53 | C2×C4 | semidirect |
| 231. #496 | Dic53 | semidirect |
| 232. #489 | Dic53 | semidirect |
| 252. C53 | #9381 | semidirect |
| 260. C4⋊Q8 | C2×Dic53 | semidirect |
| 261. #127 | C2×Dic53 | semidirect |
| 292. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277530 | 2 |
| #20275635 | 2 |
| #20273313 | 2 |
| #20273262 | 2 |
| #20272581 | 2 |
| #20272570 | 2 |
| C53×#3213 | 2 |
| #9381 | 53 |