Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #20289865 | C2 | direct (N × H) |
| 12. C2×Dic424 | C4 | semidirect |
| 16. Q32×D53 | C4 | semidirect |
| 19. C2×Q32×C53 | C4 | semidirect |
| 33. Dic424 | C2×C4 | semidirect |
| 43. Q32×C53 | C2×C4 | semidirect |
| 113. C2×C53 | #1416 | semidirect |
| 115. D53 | #1416 | semidirect |
| 125. C2×Q32 | #6157 | semidirect |
| 133. C53 | C2×#1416 | semidirect |
| 149. Q32 | C2×#6157 | semidirect |
| 225. C2 | #20289865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| C2×#16811549 | 2 |
| #20289865 | 2 |
| C2×Q32×D53 | 2 |
| C2×#1416 | 53 |