Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20287851 | C2 | semidirect |
| 2. #20287849 | C2 | semidirect |
| 3. #20285158 | C2 | semidirect |
| 4. #20276442 | C2 | semidirect |
| 5. #20275606 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 48. C2×Dic212 | D4 | semidirect |
| 55. C2×D424 | D4 | semidirect |
| 75. C2×#11719908 | D4 | semidirect |
| 92. C2×C16×C53 | D4 | semidirect |
| 232. #2143 | D53 | semidirect |
| 269. C53 | #13340 | semidirect |
| 323. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20287849 | 2 |
| #20285158 | 2 |
| #20276442 | 2 |
| #20275606 | 2 |
| #20272794 | 2 |
| C53×#2143 | 2 |
| #13340 | 53 |