Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. #20290922 | C2 | semidirect |
| 2. D53⋊#335 | C2 | semidirect |
| 3. #20289671 | C2 | semidirect |
| 4. #20289670 | C2 | semidirect |
| 30. #13133240 | C8 | semidirect |
| 71. Q16×C53 | C2×C8 | semidirect |
| 92. D424 | C2×C8 | semidirect |
| 174. C53 | #11592 | semidirect |
| 221. Q16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290922 | 2 |
| D53⋊#335 | 2 |
| #20289671 | 2 |
| #20289670 | 2 |
| C4×#13133240 | 2 |
| #11592 | 53 |