Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
12446 conjugacy classes of subgroups; only the 8971 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 8971 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 |
|---|---|---|
| 1. C22×Q8×Dic53 | C2 | direct (N × H) |
| 7. C2×Q8×Dic53 | C22 | direct (N × H) |
| 10. C23×Q8×C53 | C4 | semidirect |
| 14. C23×Dic53 | Q8 | direct (N × H) |
| 17. Q8×Dic53 | C23 | direct (N × H) |
| 21. C22×Q8×C53 | C2×C4 | semidirect |
| 29. C2×Q8×C53 | C22×C4 | semidirect |
| 34. C22×Dic53 | C2×Q8 | direct (N × H) |
| 39. C23×C53 | C4×Q8 | semidirect |
| 44. Q8×C53 | C23×C4 | semidirect |
| 48. C2×Dic53 | C22×Q8 | direct (N × H) |
| 52. C22×C53 | C2×C4×Q8 | semidirect |
| 59. Dic53 | C23×Q8 | direct (N × H) |
| 64. C2×C53 | C22×C4×Q8 | semidirect |
| 68. C23×Q8 | Dic53 | direct (N × H) |
| 76. C53 | C23×C4×Q8 | semidirect |
| 78. C22×Q8 | C2×Dic53 | direct (N × H) |
| 93. C2×Q8 | C22×Dic53 | direct (N × H) |
| 103. C23 | Q8×Dic53 | direct (N × H) |
| 108. Q8 | C23×Dic53 | direct (N × H) |
| 115. C22 | C2×Q8×Dic53 | direct (N × H) |
| 123. C2 | C22×Q8×Dic53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×Dic53 | 2 |
| C23×C4⋊Dic53 | 2 |
| C23×C4×Dic53 | 2 |
| C24×Q8×C53 | 2 |
| C23×C4×Q8 | 53 |