Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 228 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. C16×#88324 | C2 | semidirect |
| 17. D53⋊C16 | C8 | semidirect |
| 25. C16×D53 | C8 | semidirect |
| 34. D53⋊C8 | C16 | direct (N × H) |
| 44. #11719910 | C2×C8 | semidirect |
| 45. C16×C53 | C2×C8 | semidirect |
| 46. #11719908 | C2×C8 | semidirect |
| 55. #88324 | C2×C16 | semidirect |
| 75. D53 | C8×C16 | semidirect |
| 87. C53 | C2×C8×C16 | semidirect |
| 118. C16 | D53⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D53⋊C16 | 2 |
| C8×D53⋊C8 | 2 |
| C16×#88324 | 2 |
| C4×C16×D53 | 2 |
| C2×C8×C16 | 53 |