Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1614 conjugacy classes of subgroups; only the 752 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 752 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 |
|---|---|---|
| 3. #20290372 | C2 | semidirect |
| 7. #16811582 | C4 | semidirect |
| 9. C4×D53⋊C8 | C4 | semidirect |
| 21. #13133272 | C2×C4 | semidirect |
| 22. C4×#88324 | C2×C4 | semidirect |
| 81. D53 | #1726 | semidirect |
| 93. C53 | C2×#1726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811582 | 2 |
| C2×C4×D53⋊C8 | 2 |
| #20290372 | 2 |
| #376×D53 | 2 |
| C2×#1726 | 53 |