Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 251 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. C8×#11719908 | C2 | semidirect |
| 4. C16×#88322 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 19. C16×D53 | C8 | direct (N × H) |
| 36. C8×D53 | C16 | direct (N × H) |
| 38. C16×C53 | C2×C8 | semidirect |
| 39. #11719908 | C2×C8 | semidirect |
| 47. C8×C53 | C2×C16 | semidirect |
| 50. #88322 | C2×C16 | semidirect |
| 63. C8×C16 | D53 | direct (N × H) |
| 66. D53 | C8×C16 | direct (N × H) |
| 76. C53 | C2×C8×C16 | semidirect |
| 101. C16 | C8×D53 | direct (N × H) |
| 111. C8 | C16×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D53 | 2 |
| C82×D53 | 2 |
| C8×#11719908 | 2 |
| C16×#88322 | 2 |
| C8×C16×C53 | 2 |
| C2×C8×C16 | 53 |