Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
166 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 5. #16811556 | C4 | semidirect |
| 9. #16811551 | C4 | semidirect |
| 91. C53 | #7480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| D53⋊#368 | 2 |
| #20276498 | 2 |
| #7480 | 53 |