Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2190 conjugacy classes of subgroups; only the 1372 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 1372 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. #20291630 | C2 | semidirect |
| 2. #20291608 | C2 | semidirect |
| 3. #41×#88324 | C2 | semidirect |
| 4. C2×Q8×#88324 | C2 | semidirect |
| 34. 2−1+4×C53 | C8 | semidirect |
| 37. #41×C53 | C2×C8 | semidirect |
| 38. C2×Q8×C53 | C2×C8 | semidirect |
| 67. #88324 | 2−1+4 | direct (N × H) |
| 100. C53 | C8×2−1+4 | semidirect |
| 101. 2−1+4 | #88324 | direct (N × H) |
| 119. #41 | C2×#88324 | semidirect |
| 120. C2×Q8 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291630 | 2 |
| #20291608 | 2 |
| #41×#88324 | 2 |
| C2×Q8×#88324 | 2 |
| 2−1+4×Dic53 | 2 |
| C8×2−1+4 | 53 |