Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20289747 | C2 | semidirect |
| 3. #20289746 | C2 | semidirect |
| 24. C16×D53 | C8 | semidirect |
| 48. C16×C53 | C2×C8 | semidirect |
| 50. #11719908 | C2×C8 | semidirect |
| 89. D53 | #1371 | semidirect |
| 100. C53 | C2×#1371 | semidirect |
| 136. C16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#335 | 2 |
| #20289747 | 2 |
| #20289746 | 2 |
| C4×C16×D53 | 2 |
| C2×#1371 | 53 |