Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #20289676 | C2 | semidirect |
| 4. #20289675 | C2 | semidirect |
| 32. Q16×D53 | C8 | semidirect |
| 70. Q16×C53 | C2×C8 | semidirect |
| 92. Dic212 | C2×C8 | semidirect |
| 149. D53 | #1334 | semidirect |
| 167. C53 | C2×#1334 | semidirect |
| 216. Q16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290916 | 2 |
| D53⋊#334 | 2 |
| #20289676 | 2 |
| #20289675 | 2 |
| C4×Q16×D53 | 2 |
| C2×#1334 | 53 |