Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20276952 | C2 | semidirect |
| 3. #20276867 | C2 | semidirect |
| 4. #20274229 | C2 | semidirect |
| 5. #20272757 | C2 | semidirect |
| 6. #20272674 | C2 | semidirect |
| 7. C53×#1334 | C2 | semidirect |
| 78. Q16×C53 | SD16 | semidirect |
| 160. #1334 | D53 | semidirect |
| 186. C53 | #12379 | semidirect |
| 240. Q16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286371 | 2 |
| #20276952 | 2 |
| #20276867 | 2 |
| #20274229 | 2 |
| #20272757 | 2 |
| #20272674 | 2 |
| C53×#1334 | 2 |
| #12379 | 53 |