Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 192 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. #20291112 | C2 | direct (N × H) |
| 18. C2×Dic424 | C4 | semidirect |
| 19. C2×#13133163 | C4 | semidirect |
| 20. Q32×D53 | C4 | semidirect |
| 23. C2×Q32×C53 | C4 | semidirect |
| 47. Dic424 | C2×C4 | semidirect |
| 48. #13133163 | C2×C4 | semidirect |
| 53. Q32×C53 | C2×C4 | semidirect |
| 135. C2×C53 | #2176 | semidirect |
| 137. D53 | #2176 | semidirect |
| 145. C2×Q32 | #6157 | semidirect |
| 156. C53 | C2×#2176 | semidirect |
| 175. Q32 | C2×#6157 | semidirect |
| 263. C2 | #20291112 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#6157 | 2 |
| #20291112 | 2 |
| C2×#16811550 | 2 |
| C2×#16811536 | 2 |
| C2×#16811510 | 2 |
| C2×Q32×D53 | 2 |
| C2×#2176 | 53 |