Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
| 15. #13133267 | C2×C4 | semidirect |
| 84. D53 | #1398 | semidirect |
| 95. C53 | C2×#1398 | 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 |
| #346×D53 | 2 |
| C2×#1398 | 53 |