Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
7646 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C24×#88324 | C2 | semidirect |
| 2. C22×#13133274 | C2 | direct (N × H) |
| 5. C23×#88324 | C22 | semidirect |
| 6. C2×#13133274 | C22 | direct (N × H) |
| 14. C22×#88324 | C23 | semidirect |
| 15. #13133274 | C23 | direct (N × H) |
| 18. C24×D53 | C8 | semidirect |
| 37. C23×D53 | C2×C8 | semidirect |
| 50. C2×#88324 | C24 | semidirect |
| 51. C23×C53 | C22⋊C8 | semidirect |
| 59. C22×D53 | C22×C8 | semidirect |
| 71. C22×C53 | C2×C22⋊C8 | semidirect |
| 79. C2×D53 | C23×C8 | semidirect |
| 86. C2×C53 | C22×C22⋊C8 | semidirect |
| 100. C53 | C23×C22⋊C8 | semidirect |
| 144. C23 | #13133274 | direct (N × H) |
| 162. C22 | C2×#13133274 | direct (N × H) |
| 171. C2 | C22×#13133274 | 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×#13133274 | 2 |
| C24×C4×D53 | 2 |
| C23×C22⋊C8 | 53 |