Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2046 conjugacy classes of subgroups; only the 1227 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1227 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. C42×#88322 | C2 | semidirect |
| 4. C4×C8×Dic53 | C2 | semidirect |
| 5. C42×C8×C53 | C2 | semidirect |
| 11. C4×C8×D53 | C4 | direct (N × H) |
| 23. C42×D53 | C8 | direct (N × H) |
| 25. C4×#88322 | C2×C4 | semidirect |
| 26. C8×Dic53 | C2×C4 | semidirect |
| 30. C4×C8×C53 | C2×C4 | semidirect |
| 40. C42×C53 | C2×C8 | semidirect |
| 43. C4×Dic53 | C2×C8 | semidirect |
| 46. C8×D53 | C42 | direct (N × H) |
| 56. C4×D53 | C4×C8 | direct (N × H) |
| 58. C8×C53 | C2×C42 | semidirect |
| 59. #88322 | C2×C42 | semidirect |
| 65. C4×C53 | C2×C4×C8 | semidirect |
| 68. Dic53 | C2×C4×C8 | semidirect |
| 73. C42×C8 | D53 | direct (N × H) |
| 76. D53 | C42×C8 | direct (N × H) |
| 87. C53 | C2×C42×C8 | semidirect |
| 102. C4×C8 | C4×D53 | direct (N × H) |
| 117. C42 | C8×D53 | direct (N × H) |
| 131. C8 | C42×D53 | direct (N × H) |
| 138. C4 | C4×C8×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×D53 | 2 |
| C43×D53 | 2 |
| C42×#88322 | 2 |
| C4×C8×Dic53 | 2 |
| C42×C8×C53 | 2 |
| C2×C42×C8 | 53 |