Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3870 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 3870 conjugacy classes of subgroups — too many to draw. Only its 2232 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 |
|---|---|---|
| 2. C22×C4⋊#88324 | C2 | direct (N × H) |
| 6. C2×C4⋊#88324 | C22 | direct (N × H) |
| 14. C4⋊#88324 | C23 | direct (N × H) |
| 24. C23×C4×C53 | C8 | semidirect |
| 30. C22×C4×C53 | C2×C8 | semidirect |
| 43. C23×C53 | C4⋊C8 | semidirect |
| 48. C2×C4×C53 | C22×C8 | semidirect |
| 59. C22×C53 | C2×C4⋊C8 | semidirect |
| 64. C4×C53 | C23×C8 | semidirect |
| 72. C2×C53 | C22×C4⋊C8 | semidirect |
| 84. C53 | C23×C4⋊C8 | semidirect |
| 92. C23×C4 | #88324 | semidirect |
| 110. C22×C4 | C2×#88324 | semidirect |
| 116. C23 | C4⋊#88324 | direct (N × H) |
| 128. C2×C4 | C22×#88324 | semidirect |
| 131. C22 | C2×C4⋊#88324 | direct (N × H) |
| 140. C4 | C23×#88324 | semidirect |
| 141. C2 | C22×C4⋊#88324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#88324 | 2 |
| C22×C4⋊#88324 | 2 |
| C23×C4×Dic53 | 2 |
| C23×C4⋊C8 | 53 |