Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 112 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. #20289827 | C2 | semidirect |
| 3. #20289826 | C2 | semidirect |
| 5. #16811556 | C4 | semidirect |
| 7. D53⋊C32 | C4 | semidirect |
| 85. C53 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| #20289827 | 2 |
| #20289826 | 2 |
| #20276310 | 2 |
| #13551 | 53 |