Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20277825 | C2 | semidirect |
| 3. #20273338 | C2 | semidirect |
| 4. #20273223 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1505 | C2 | semidirect |
| 11. #16811015 | C4 | semidirect |
| 12. #16811010 | C4 | semidirect |
| 58. #13133128 | C2×C4 | semidirect |
| 66. C4⋊Q8×C53 | C2×C4 | semidirect |
| 67. #127×C53 | C2×C4 | semidirect |
| 224. #1505 | D53 | semidirect |
| 257. C53 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D53 | semidirect |
| 272. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285183 | 2 |
| #20277825 | 2 |
| #20273338 | 2 |
| #20273223 | 2 |
| #20272608 | 2 |
| #20272607 | 2 |
| C53×#1505 | 2 |
| #9441 | 53 |