Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 360 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 |
|---|---|---|
| 6. #16811464 | C4 | direct (N × H) |
| 19. C4×#88322 | C8 | semidirect |
| 20. C8×Dic53 | C8 | semidirect |
| 24. C4×C8×C53 | C8 | semidirect |
| 54. C8×C53 | C4×C8 | semidirect |
| 55. #88322 | C4×C8 | semidirect |
| 61. C4×C53 | #322 | semidirect |
| 64. Dic53 | #322 | semidirect |
| 81. C53 | C4×#322 | semidirect |
| 94. C4×C8 | #88324 | semidirect |
| 125. C8 | C4×#88324 | semidirect |
| 132. C4 | #16811464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#88324 | 2 |
| C2×#16811464 | 2 |
| C4×C8×Dic53 | 2 |
| C4×#322 | 53 |