Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4830 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 744 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. #20289905 | C2 | direct (N × H) |
| 7. C23×Dic106 | C4 | semidirect |
| 9. C22×Q8×D53 | C4 | semidirect |
| 12. C23×Q8×C53 | C4 | semidirect |
| 15. C23×#6157 | Q8 | semidirect |
| 21. C22×Dic106 | C2×C4 | semidirect |
| 31. C22×Q8×C53 | C2×C4 | semidirect |
| 44. C22×#6157 | C2×Q8 | semidirect |
| 108. C2×C53 | #1446 | semidirect |
| 111. D53 | #1446 | semidirect |
| 118. C23×Q8 | #6157 | semidirect |
| 123. C53 | C2×#1446 | semidirect |
| 132. C22×Q8 | C2×#6157 | semidirect |
| 218. C2 | #20289905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×#6157)⋊C4 | 2 |
| #20289905 | 2 |
| C23×Q8×D53 | 2 |
| C2×#1446 | 53 |