Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 136 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. #20289675 | C2 | direct (N × H) |
| 45. C2×Q16×C53 | C8 | semidirect |
| 61. Q16×C53 | C2×C8 | semidirect |
| 122. C2×C53 | #1334 | semidirect |
| 141. C53 | C2×#1334 | semidirect |
| 145. C2×Q16 | #88324 | semidirect |
| 181. Q16 | C2×#88324 | semidirect |
| 239. C2 | #20289675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811512 | 2 |
| C2×#16811484 | 2 |
| #20289675 | 2 |
| C2×Q16×Dic53 | 2 |
| C2×#1334 | 53 |